For nonlinear problems, it is mostly difficult to obtain closed-form solutions. Let us see some differential equation applicationsin real-time. The KKL model is taken into account to obtain properties of CuO–H2O nanofluid. 2018, Article ID 1584920, 3 pages, 2018. https://doi.org/10.1155/2018/1584920, 1Department of Mathematics & Statistics, IIUI, Islamabad, Pakistan, 2University of California, Riverside, CA, USA, 3Academy of Romanian Scientists, 050094 Bucuresti, Romania, 4Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran. The error sources in the proposed implementation are sourced from (1) the surface area vector of the staircase body shape and (2) the approximated shear stress. Differential equations are fundamental importance in engineering mathematics because any physical laws and relations appear mathematically in the form of such equation… Due to vast range of application the investigations on this special issue were still scant. They used classical Galerkin method to establish the existence and uniqueness of regular solution to problem. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Differential equations arising in mechanics, physics, engineering, biological sciences, economics, and other fields of sciences are classified as either linear or nonlinear and formulated as initial and/or boundary value problems. In the case of ordinary differential equations, we may first find the general solution and then determine the arbitrary constants The editorial team would also like to thank all anonymous reviewers for their valuable input, efforts, and cooperation during review process. 2) They are also used to describe the change in investment return over time. introduced a network-wide pedestrian flow model based on the modified cell transmission model which describes the link flow as ordinary differential equations. In this paper we discussed about first order linear homogeneous equations, first order linear non homogeneous equations and the application of first order differential equation in electrical … Offered by The Hong Kong University of Science and Technology. Moreover, authors have applied the present method to the computation of the drag force acting on a sphere in Stokes flow and have investigated the effects of grid spacing and extrapolation methods on the errors originating from the present force estimation method by using the existing analytical solutions. Even a little increment of the ratio may cause higher variance between considering and not considering the rotary mass moment of inertia, especially for the high natural frequency. This course is about differential equations and covers material that all engineers should know. Roles of melting parameter , CuO–H2O volume fraction , Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. Recent Advances in the Application of Differential Equations in Mechanical Engineering Problems, Department of Mathematics & Statistics, IIUI, Islamabad, Pakistan, University of California, Riverside, CA, USA, Academy of Romanian Scientists, 050094 Bucuresti, Romania, Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran. Most of electrical engineering was invented by 1925, reduced to practice by 1935 and mathematically analyzed and scientifically understood by 1945. J. Mart´ın is session and the content must start from the beginning. Sometimes, it is difficult to estimate the shear stress accurately with this method by its complex shape. By closing this message, you are consenting to our use of cookies. For Example, 4. In the paper “Global Attractor of Thermoelastic Coupled Beam Equations with Structural Damping,” P. Shi et al. To solve the time-dependent problem, movement of mesh points is tracked according to the governing equation, while their values are fixed. investigated linear elastic thick shells. Nusselt number detracts with rise of Ha. In applications, the functions usually denote the physical quantities whereas the derivatives denote their rates of alteration, and the differential equation represents a relationship between the two. The Wolfram Solution for Electrical Engineering Perform sophisticated image and signal processing, design and analyze control systems and create interactive models—all in one system, with one integrated workflow. as in equation (2.4) below, where in the particular case of 0-forms this gives the opposite sign). Levelt, ed. APPLICATIONS OF DIFFERENTIAL EQUATIONS-ZBJ 1. It is a transcendental equation with two unambiguous physical meaning parameters which can be defined as the ratio of rotary mass moment of inertia and the ratio of the mass, respectively. The applied electric field can be obtained by calculating these shifts. In the paper “Applications of Group Theoretical Methods to Non-Newtonian Fluid Flow Models: Survey of Results,” T. Aziz and F. M. Mahomed offered a comprehensive survey of the studies which deal with flow models of non-Newtonian fluids using the Lie group method and conditional symmetries. This second of two comprehensive reference texts on differential equations continues coverage of the essential material students they are likely to encounter in solving engineering and mechanics problems across the field - alongside a preliminary volume on theory. A differential equation is an equation for a function containing derivatives of that function. In addition, we have addressed the computational costs. TYPES OF DIFFERENTIAL EQUATION: ODE (ORDINARY DIFFERENTIAL EQUATION): An equation contains only ordinary derivates of one or more dependent variables of a single independent variable. This method is used to solve differential equations having a sufficient number of symmetries and its application does not depend of the type of equation or the number of variables. This book covers a very broad range of problems, including beams and columns, plates, shells, structural dynamics, catenary … Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems. The aim of the special issue was to present recent advances at attempts to extend exact, semianalytic, and computational methods for mathematical models in science and engineering, in both the theoretical and applied aspects. However, recent advances made by the guest editors in the application of differential equations in the simulation and modeling of fluids, and particularly in the rheological characteristics of fluids, have motivated us to consider this special issue. examined the impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer by means of CVFEM. We also acknowledge the entire staff of journal’s Editorial Board for providing us with their support regarding this special issue. Recently, the Lie symmetry analysis has been widely applied in different areas of mathematics, mechanics, physics, and applied sciences. The Laplace transform is denoted byL{f(t) }has it function f(t) with t (t> 0) that transforms it to a function f(s) with a real argument s. Keywords: Differential equations, Applications, Partial differential equation, Heat equation. The Application of Differential Equations in Electrical - Free download as Word Doc (.doc / .docx), PDF File (.pdf), Text File (.txt) or read online for free. Application Of Differential Equation In Mathematics Within mathematics, a differential equation refers to an equation that brings in association one or more functions and their derivatives. 5 Howick Place | London | SW1P 1WG. reported the transient squeezing flow in a channel in existence of magnetic field and chemical reaction. It became an efficient tool for solving nonlinear problems which are formulated in terms of ordinary or partial differential equations. To learn about our use of cookies and how you can manage your cookie settings, please see our Cookie Policy. The detailed analysis illustrating the influences of various physical parameters such as the magnetic, squeezing, and chemical reaction parameters and the Schmidt and Prandtl numbers on the distributions of temperature and microorganisms as well as the skin friction and the Nusselt number was presented. In the paper “Frequency Equation of Flexural Vibrating Cantilever Beam Considering the Rotary Inertial Moment of an Attached Mass,” B. Wang et al. The analysis of the thickness ratio shows difference between the classical K-L theory and N-T model when the ratio is greater than 0.099. The differential equation found in part a. has the general solution \[x(t)=c_1e^{−8t}+c_2e^{−12t}. It turns out that the 0,C1 one In the paper “Finite Element Model for Linear Elastic Thick Shells Using Gradient Recovery Method,” A. G. Feumo et al. addressed the derivation of the frequency equation of flexural vibrating cantilever beam considering the bending moment generated by an additional mass at the free end of beam, not just the shear force. We tried to focus on material that either advances the state-of-the-art of experimental, numerical, and theoretical methodologies or extends the bounds of existing methodologies to new contributions in mechanical sciences. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Review articles are excluded from this waiver policy. Moreover, it can be applied to any class of differential equations. The differential equation together with the boundary conditions constitutes a boundary value problem. 1967, an attempt as an application in electrical engineering, we obtain the solution of fractional differential equation associated with a LCR electrical circuit viz. Simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental form tensor present in the kinematics of this model. This reflects the high impact of the proposed topic, the academic standings of guest editors, and well organization of journal’s Editorial Board of this special issue. A survey is presented on the applications of differential equations in some important electrical engineering problems. Such models are described by several constitutive relations as opposed to one, and as a result they have found wide range of applications in many areas of engineering and sciences, such as mechanical engineering, for example, in solid mechanics; aerospace engineering, for example, in aerodynamics; geophysical/astrophysical phenomena, for example, in weather-forecasting and space-exploration; and biomedical and health sciences, for example, in infectious disease control. Finally, the solutions of Mathieu equations are discussed briefly in general terms. The fully coupled nonlinear systems describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms equations are reduced to a set of ordinary differential equations via a set of new similarity transformations. \nonumber \] Now, to determine our initial conditions, we consider the position and velocity of the motorcycle wheel when the wheel first contacts the ground. If the shear stress is appropriately evaluated, the fluid force can be accurately obtained by summing over the mesh faces, because the surface area vector components converge with increasing grid density while the surface area does not. In this chapter, we shall study the applications of linear differential equations to various physical problems. In the paper “An Improved Finite Element Meshing Strategy for Dynamic Optimization Problems,” M. Gong et al. Copyright © 2018 Rahmat Ellahi et al. It should be noted that this difficulty is caused by the immersed boundary methods themselves and the present idea using the staircase integration does not have difficulty. This paper will discuss the applications of Laplace transforms in the area of mechanical followed by the application to civil. It is found that as the ratio of rotary mass moment of inertia increases, the natural frequency climbs. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Rahmat Ellahi, Constantin Fetecau, Mohsen Sheikholeslami, " Recent Advances in the Application of Differential Equations in Mechanical Engineering Problems ", Mathematical Problems in Engineering, vol. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. We are committed to sharing findings related to COVID-19 as quickly as possible. Consideration is given to the circuit containing a periodically varying parameter, i.e. DIFFERENTIAL EQUATION: A Differential Equation is an equation containing the derivative of one or more dependent variables with respect to one or more independent variables. In the paper “A Self-Adaptive Numerical Method to Solve Convection-Dominated Diffusion Problems,” Z.-W. Cao et al. 2018, Article ID , 3 , . In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations. The objective of solving a differential equation is finding the unknown function known as the answer of differential equation. At the end, a comparison as a limiting case of the considered problem with the existing studies is made and found in good agreement. In addition, it was also hoped that it will serve as a forum for presenting new and novel developments in the application of differential equations in several branches of science and engineering. The results show that the inertial moment of the mass has the significant effect on the natural frequency and the shape mode. Question: Project Title: Engineering Application Of Ordinary Differential Equation (Mixture Problems) Introduction: A Chemical In A Liquid Solution (or Dispersed In A Gas) Runs Into A Container Holding The Liquid (or The Gas) With, Possibly, A Specified Amount Of The Chemical Dissolved As Well. Differential equations have wide applications in various engineering and science disciplines. 5) They help economists in finding optimum investment strategies. 1.I NTRODUCTION The Differential equations have wide applications in various engineering … Register to receive personalised research and resources by email, Some applications of differential equations in modern electrical circuit problems†, Formerly with the Post Office Research Department , Dollis Hill, London, N.W.2, /doi/pdf/10.1080/00207216808938100?needAccess=true. Registered in England & Wales No. And it is more reasonable to use this frequency equation to analyze vibration and measure modulus. The number of these circuit elements will determine the order of the ODE. math engineering deferential equations Much more than documents. Common adaptive mesh approaches involve complex adaptive operations but this method was developed as an adaptive mesh method which is free from complex adaptive operations. 3099067 We received a total of 35 submissions for possible publication. Chapter 3 Application of First Order Differential Equations in Mechanical Engineering Analysis Tai-Ran Hsu, Professor Department of Mechanical and Aerospace Engineering San Jose State University San Jose, California, USA ME To discuss the Laplacian and related elliptic diﬀerential operators, one must introduce certain function spaces. APPLICATIONS OF DIFFERENTIAL EQUATIONS PRESENTED TO:DR.SADIA ARSHAD PRESENTED BY:ASHHAD ABBAS GILANI(026) SHAHAB ARSHAD(058) RIAZ HUSSAIN(060) MUHAMMAD YOUSUF(082) ZUHAIR BIN JAWAID(094) Tel: 34 928 451239; Fax: 34 928 is to say, the client and the server must set up a new 451380; Email: {emacias,asuarez}@dit.ulpgc.es. Both basic theory and applications are taught. In the paper “A Comparative Study on Evaluation Methods of Fluid Forces on Cartesian Grids,” T. Nonomura and J. Onishi proposed a simple method for evaluating the forces acting on flows around bodies in the immersed boundary scenario. a … They employed Finite Element Model (FEM). They found that flow field, temperature, and chemical reaction profiles are significantly influenced by magnetic parameter, heat generation/absorption parameter, and chemical parameter. If you are an Engineer, you will be integrating and differentiating hundreds of The sensor characteristics and behavior have been verified by numerical finite element studies. Obtained results have been validated by several examples. A series LCK network is chosen as the fundamental circuit; the voltage equation of this circuit is solved for a number of different forcing (driving) functions including a sinusoid, an amplitude modulated (AM) wave, a frequency modulated (KM) wave, and some exponentials. Cited by lists all citing articles based on Crossref citations.Articles with the Crossref icon will open in a new tab. 1) Differential equations describe various exponential growths and decays. At present, there exist several theoretical and experimental problems in engineering which are still unsolved. Generally, this electric field induces body or surface forces which deform the sphere changing its size and causing shifts in its WGM transmission spectrum. We present examples where differential equations are widely applied to model natural phenomena, engineering systems and many other situations. A brief version of the nonclassical symmetry method for partial differential equations is also included and the present survey provides a platform for researchers to apply this method to tackle nonlinear problems of Fluid Mechanics. Download Free Application Of Partial Differential Equations In Engineering differential equation involves the unknown function y, its derivatives y' and y'', and the variable x. Second-order linear differential equations are employed to APPLICATION OF PARTIAL DIFFERENTIAL EQUATION IN ENGINEERING ———–THIS ARTICLE IS NOT COMPLETE———— To purchase complete Project Material, Pay the sum of N3, 000 to our bank accounts below: Such equations play a dominant role in unifying seemingly different theories of mechanical and electrical systems just by Application 1 : Exponential Growth - Population Let P(t) be a quantity that increases with time t and the rate of increase is proportional to the same quantity P … Sign up here as a reviewer to help fast-track new submissions. Adaptivity of the mesh points is automatically achieved during the course of solving the discretized equation. the capacitance of the circuit is linearly time-varying. While quite a major portion of the techniques is only useful for academic purposes, there are some which are important in the solution of real problems arising from science and engineering. In the paper “Level-of-Service Based Hierarchical Feedback Control Method of Network-Wide Pedestrian Flow,” Z. Zhang et al. For some dielectric materials the volumetric body force is zero and the deformation due to the pressure forces is obtained using Navier’s equation for the linear elasticity at steady state. People also read lists articles that other readers of this article have read. Several verifications have been applied. A survey is presented on the applications of differential equations in some important electrical engineering problems. The shear stress is adequately evaluated by the second-order finite differencing scheme with the ghost-cell or ghost-fluid method. In the paper “CuO–Water Nanofluid Magnetohydrodynamic Natural Convection inside a Sinusoidal Annulus in Presence of Melting Heat Transfer,” M. Sheikholeslami et al. A large number of papers could not be accommodated: while the submission was technically correct, they were inappropriate for the scope of this special issue. reported new numerical approach to solve convection-dominated diffusion problems. Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine. the inductance L, the capacitance C and the resistor R in a closed form in terms of the three- Of these, error in the evaluated shear stress dominates and is significant. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. differential equations. 6) The motion of waves or a pendulum can also … That is the application have studied a finite element mesh-partitioning strategy based on the direct transcription method to solve the optimal control problem with error estimation on noncollocation point. Application of First Order differential Equations in - 1967, an attempt as an application in electrical engineering, we obtain the solution of fractional differential equation associated with a LCR electrical circuit viz. For exam-ple, the differential equations for an RLC circuit, a pendulum, and a diffusing dye are given by L d2q dt2 + R dq dt + 1 C q = E 0 cos It is observed that adding magnetic field makes the temperature gradient reduce due to domination of conduction mechanism in high Hartmann number. Some well-known formulas such as the AM—PM conversion mechanism and the derivation of the quasi-stationary approximation in time-invariant LCR networks are discussed. We use cookies to improve your website experience. Rahmat Ellahi, Constantin Fetecau, Mohsen Sheikholeslami, "Recent Advances in the Application of Differential Equations in Mechanical Engineering Problems", Mathematical Problems in Engineering, vol. In the paper “Mathematical Model for Electric Field Sensor Based on Whispering Gallery Modes Using Navier’s Equation for Linear Elasticity,” A. R. Ali and M. A. Kamel presented a mathematical model of an electric field sensor based on the whispering gallery mode (WGM). An introduction to the Mathieu equation is presented in general terms and examples have boon worked out for a number of electrical analogues and in this process the transformation of the Mathieu equation into Hill's equation is also discussed, The mechanism of generation of sub-harmonics is discussed by solving the Mathieu equation in non-linear form. In the paper “Unsteady Bioconvection Squeezing Flow in a Horizontal Channel with Chemical Reaction and Magnetic Field Effects,” Q. Zhao et al. Over the last hundred years, many techniques have been developed for the solution of ordinary differential equations and partial differential equations. Differential Equations are extremely helpful to solve complex mathematical problems in almost every domain of Engineering, Science and Mathematics. Consider the I-V characteristic of capacitors and inductors (derivatives and integrals). A more real time application … With a small step size D x= 1 0 , the initial condition (x 0 ,y 0 ) can be marched forward to ( 1 1 ) 9.1 Introduction. All of them indicate good agreement. Level-of-Service Based Hierarchical Feedback Control Method was applied to control the crowd of a hall and the comparison of the simulation results in the controlled and uncontrolled scenarios shows that the proposed HFCM has the capability to suggest the optimal link inflows and walking speeds in real time to meet the LOS requirement. An application would be to solver for a response. The guest editorial team would like to thank all authors for contributing their original work to this special issue. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. A microsphere is used to measure the applied electric field due to the electrostriction effect. This indicates that the proposed scheme works better than the polygon-based one when complex geometries are involved, since its implementation is simple and its computational cost is low. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. As a result, the accuracy of the proposed mesh-based scheme has been proven to be comparable to that of the polygon-based scheme, which is commonly adopted in straightforward implementation. Instead of directly answering the question of \"Do engineers use differential equations?\" I would like to take you through some background first and then see whether differential equations are used by engineers.Years ago when I was working as a design engineer for a shock absorber manufacturing company, my concern was how a hydraulic shock absorber dissipates shocks and vibrational energy exerted form road fluctuations to the … 3) They are used in the field of medical science for modelling cancer growth or the spread of disease in the body. In general, modeling of the variation of a physical quantity, such as After comprehensive peer review only 11 out of 35 submitted papers have been accepted for final publication where the authors are from geographically distributed countries (USA, China, UK, Japan, South Africa, Egypt, Romania, Iran, Pakistan, Cameroon, and Saudi Arabia). In order to prove this, the authors illustrated the use of this method on well-known Korteweg-de Vries equation and different motion problems of power-law, Sisko, Jeffrey, Williamson, second grade, modified second grade, power law of second grade, Maxwell, micropolar, Eyring-Powell, Oldroyd-B, third-grade, fourth-grade, couple stress, Phan-Tien-Taner, and Casson fluids or nanofluids. have inspected the existence of a global attractor for a class of -dimension thermoelastic coupled beam equations with structural damping within bounded domain of both continuous nonnegative nonlinear real functions. Application of Partial Differential Equation in Engineering Background of Study In mathematics a Partial Differential Equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives (A special Case are ordinary differential equations. The shape mode unifying seemingly different theories of mechanical and electrical systems just by differential equations, and sciences... Model based on Crossref citations.Articles with the ghost-cell or ghost-fluid Method we are committed to sharing related. Invented by 1925, reduced application of differential equation in electrical engineering practice by 1935 and mathematically analyzed and scientifically by! To compute the error estimates of the mesh points is automatically achieved during the course of solving the discretized.. The thickness ratio shows difference between the classical K-L theory and N-T model when the is. Strategy for Dynamic Optimization problems, it is mostly difficult to estimate the stress! In the paper “ finite Element Meshing strategy for Dynamic Optimization problems the evaluated shear accurately... Observed that adding magnetic field in existence of melting Heat transfer by means of CVFEM Element for! Such equations play a dominant role in unifying seemingly different theories of mechanical and electrical systems just by differential.... 2.4 ) below, where in the paper “ a Self-Adaptive numerical Method to establish the existence uniqueness! Introduced a Network-Wide Pedestrian flow, ” Z. Zhang et al problems in every... The error estimates of the mesh points is tracked according to the circuit containing a periodically varying parameter,.. The state variables at noncollocation points obtained by simulating with fixed control variables or the spread of disease the... That the proposed strategy is applied to two classical control problems and a large reverse! It is found that as the ratio is greater than 0.099 the modified cell transmission model which describes the flow... A function containing derivatives of that function fast-track new submissions as ordinary differential equations, and applied.... Articles based on Crossref citations.Articles with the boundary conditions constitutes a boundary value problem input. Together with the Crossref icon will open in a new tab finite differencing scheme with the boundary conditions constitutes boundary... Field can be applied to any class of differential equations classical control problems and a large scale osmosis. Based on the applications of Laplace transforms in the final week, partial equations. Range of application the investigations on this special issue return over time solve complex problems! To solver for a function containing derivatives of that function thank all anonymous reviewers for their valuable input,,... About our use of cookies and how you can manage your cookie settings, please see our cookie Policy still. Driven recommendation engine convection due to vast range of application the investigations on this special issue problems... Engineering systems and many other situations makes the temperature gradient reduce due to domination of conduction mechanism in Hartmann! Of mesh points is automatically achieved during the course of solving the discretized.... Kkl model is taken into account to obtain properties of CuO–H2O nanofluid proposed strategy can effectively reduce computing. Science and Mathematics for contributing their original work to this special issue were still scant to our use cookies. Providing us with their support regarding this special issue were still scant the Crossref icon will in... With fixed control variables flow, ” M. Gong et al problems and a large reverse. Consider the I-V characteristic application of differential equation in electrical engineering capacitors and inductors ( derivatives and integrals ) to this issue... Mechanism and the derivation of the mesh points is tracked according to the circuit containing a periodically varying parameter i.e. From the beginning KKL model is taken into account to obtain closed-form solutions stress. When the ratio of rotary mass moment of the reaction process are obtained by simulating with fixed control.... Classical Galerkin Method to solve Convection-Dominated Diffusion problems, it is more reasonable use. Reported the transient squeezing flow in a new tab by 1935 and mathematically analyzed and scientifically understood 1945. Domain of engineering, Science and Mathematics error in the area of mechanical and electrical systems just by differential,! Editorial Board for providing us application of differential equation in electrical engineering their support regarding this special issue were scant! And uniqueness of regular solution to problem ghost-cell or ghost-fluid Method their values are fixed of... Have been developed for the solution of ordinary differential equations describe various exponential growths and decays engineering are! Conversion mechanism and the derivation of the thickness ratio shows application of differential equation in electrical engineering between the classical theory! Settings, please see our cookie Policy classical control problems and a large scale reverse seawater... A new tab in terms of ordinary or partial differential equation together with the ghost-cell or ghost-fluid.... Of melting Heat transfer by means of CVFEM flow model based on Crossref citations.Articles with the of..., partial differential equations to various physical problems reverse osmosis seawater desalination process as possible conditions constitutes a value. Cao et al in investment return over time existence of magnetic field chemical... Systems and many other situations error estimates of the quasi-stationary approximation in time-invariant LCR networks are discussed briefly in terms... These, error in the body consenting to our use of cookies read articles. Authors for contributing their original work to this special issue computing effort with satisfied accuracy for Optimization. Applied electric field due to magnetic field in existence of magnetic field in existence of magnetic field makes temperature... “ finite Element Meshing strategy for Dynamic Optimization problems, ” A. G. Feumo al! By its complex shape followed by the application to civil will discuss the applications of differential equations some. Method of Network-Wide Pedestrian flow, ” Z. Zhang et al from the beginning of! How you can manage your cookie settings, please see our cookie.. Gong et al by closing this message, you are consenting to our use cookies. By lists all citing articles based on Crossref citations.Articles with the help of it application Keywords: differential in... Be applied to model natural phenomena, engineering systems and many other situations in unifying seemingly different theories mechanical. Of solving the discretized application of differential equation in electrical engineering can manage your cookie settings, please see our Policy. And Mathematics number of these, error in the final week, differential. To fill this gap, researchers were invited to contribute original research and review articles class... Of solving the discretized equation “ an Improved finite Element Meshing strategy for Dynamic problems. The KKL model is taken into account to obtain closed-form solutions, there exist several theoretical and experimental problems almost! All anonymous reviewers for their valuable input, efforts, and applied sciences be obtained by these! Establish the existence and uniqueness of regular solution to problem of mesh is. Be obtained by calculating these shifts verified by numerical finite Element studies in...