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The purpose of this paper is to obtain approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions, by the homotopy analysis method (HAM).

The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions.

Approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions is obtained by the HAM. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions.

In this work, approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions is obtained by the HAM. To show the efficiency of the present method, several examples are presented.

The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation.

In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives.

The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy.

The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method.

The authors used Maple Package to calculate the solutions obtained from the homotopy Padé method.

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m, m] homotopy Padé technique are often independent of auxiliary parameter h and this technique accelerates the convergence of the related series. Finally, numerical results for some test problems with known solutions are presented and the numerical results are given to show the efficiency of the proposed techniques.

The paper is shown that homotopy Padé technique is a promising tool with accelerated convergence for complicated nonlinear differential equations.

The main purpose of this work is the development of a numerical algorithm based on modified cubic trigonometric B-spline functions for computational modelling of hyperbolic-type wave equations. These types of equations describe a variety of physical models in the vibrations of structures, nonlinear optics, quantum field theory and solid-state physics, etc.

Dirichlet boundary conditions cannot be handled easily by cubic trigonometric B-spline functions. Then, a modification is made in cubic trigonometric B-spline functions to handle the Dirichlet boundary conditions and a numerical algorithm is developed. The proposed algorithm reduced the hyperbolic-type wave equations into a system of first-order ordinary differential equations (ODEs) in time variable. Then, stability-preserving SSP-RK54 scheme and the Thomas algorithm are used to solve the obtained system. The stability of the algorithm is also discussed.

A different technique based on modified cubic trigonometric B-spline functions is proposed which is quite different from the schemes developed (Abbas et al., 2014; Nazir et al., 2016) and depicts the computational modelling of hyperbolic-type wave equations.

To the best of the authors’ knowledge, this technique is novel for solving hyperbolic-type wave equations and the developed algorithm is free from quasi-linearization process and finite difference operators for time derivatives. This algorithm gives better results than the results discussed in literature (Dehghan and Shokri, 2008; Batiha et al., 2007; Mittal and Bhatia, 2013; Jiwari, 2015).

We consider here a general nerwork composed by n‐distributed parameters lines (with telegraph‐equations models) and m‐capacitors, all connected by a resistive multiport. An asymptotic stability property drives us to define and evaluate a global parameter (“λ‐delay time”) which describes the speed of signals propagation through the network. Because of its simplicity of calculation and its tightness, the given upper bound of the λ‐delay time is useful in timing analysis of MOS integrated chips.

The purpose of this study is to develop an algorithm for approximate solutions of nonlinear hyperbolic partial differential equations.

In this paper, an algorithm based on the Haar wavelets operational matrix for computational modelling of nonlinear hyperbolic type wave equations has been developed. These types of equations describe a variety of physical models in nonlinear optics, relativistic quantum mechanics, solitons and condensed matter physics, interaction of solitons in collision-less plasma and solid-state physics, etc. The algorithm reduces the equations into a system of algebraic equations and then the system is solved by the Gauss-elimination procedure. Some well-known hyperbolic-type wave problems are considered as numerical problems to check the accuracy and efficiency of the proposed algorithm. The numerical results are shown in figures and Linf, RMS and L2 error forms.

The developed algorithm is used to find the computational modelling of nonlinear hyperbolic-type wave equations. The algorithm is well suited for some well-known wave equations.

This paper extends the idea of one dimensional Haar wavelets algorithms (Jiwari, 2015, 2012; Pandit et al., 2015; Kumar and Pandit, 2014, 2015) for two-dimensional hyperbolic problems and the idea of this algorithm is quite different from the idea for elliptic problems (Lepik, 2011; Shi et al., 2012). Second, the algorithm and error analysis are new for two-dimensional hyperbolic-type problems.

The purpose of this paper is to offer a simulation method for predicting the impedance of machine windings at higher frequencies.

A transmission‐line model (TLM) is developed based on parameters calculated on the basis of electroquasistatic and magnetoquasistatic finite‐element (FE) model of the winding cross‐section.

The FE formulations for the low‐ and high‐frequency limits give acceptable results for the respective frequency ranges. An eddy‐current formulation is only accurate on a broader region when the FE mesh is sufficiently fine to resolve the skin depth.

The paper is restricted to frequency‐domain simulations.

The results of the paper improve the understanding of higher‐frequency parasitic effects in electrical drives with long windings.

The paper shows the limitations of the FE methods used for determining the parameters of the TLMs and remedies to avoid these.

This paper aims to present a general framework of the homotopy perturbation method (HPM) for analytic treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense.

Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation and fractional Klein‐Gordon equation are investigated to show the pertinent features of the technique.

HPM is a powerful and efficient technique in finding exact and approximate solutions for fractional partial differential equations in fluid mechanics. The implementation of the noise terms, if they exist, is a powerful tool to accelerate the convergence of the solution. The results so obtained reinforce the conclusions made by many researchers that the efficiency of the HPM and related phenomena gives it much wider applicability.

The essential idea of this method is to introduce a homotopy parameter, say p, which takes values from 0 to 1. When p = 0, the system of equations usually reduces to a sufficiently simplied form, which normally admits a rather simple solution. As p is gradually increased to 1, the system goes through a sequence of deformations, the solution for each of which is close to that at the previous stage of deformation.

The purpose of this paper is to propose a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two-space-dimensional quasilinear hyperbolic partial differential equations subject to appropriate Dirichlet and Neumann boundary conditions.

The PDQM reduced the equations into a system of second order linear differential equation. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations.

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions. The proposed technique can be applied easily for multidimensional problems.

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points and the problem can be solved up to big time. The good thing of the present technique is that it is easy to apply and gives us better accuracy in less numbers of grid points as comparison to the other numerical techniques.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.