Numerical solution of telegraph equation using interpolating scaling functions

Lakestani, Mehrdad; Saray, Behzad Nemati

doi:10.1016/j.camwa.2010.07.030

Cited by 105 publications

(74 citation statements)

References 19 publications

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“…It is evident from the solution process that the present method provides a good approximate solution in comparison with the exact solution. Also comparison made with the results obtained by Lakestani and Nemati Saray [8] and Javidi [31]. As can be seen from tables, the present method, considerably more accurate than the other methods.…”

Section: Discussionmentioning

confidence: 52%

“…(26) we have Table 1 show the absolute error |u(1, t) − u n (1, t)| using the LHPM with α = 20, β = 10 for various values of n and t. As can be seen from the table, the numerical solutions are in good agreement with the exact solution. In Table 2, we list the results obtained by LT-HPM method and compared with the results given in Lakestani and Nemati Saray [8], with β = 10, α = 20 for various values of x and t. As we seen from this table, it is clear that the results obtained by LT-HPM is superior to that obtained by Lakestani and Nemati Saray [8].…”

Section: Numerical Resultsmentioning

confidence: 92%

“…Abdou [7], used Adomian decomposition method for solving the telegraph equation in charged particle transport. Lakestani and Saray [8], developed a numerical technique for the solution of second order one dimensional linear hyperbolic equation. The method consists of expanding the required approximate solution as the elements of interpolating scaling functions.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Telegraph Equation by Using LT Inversion Technique

Javidi

Nyamoradi

2013

International Journal of Advanced Mathematical Sciences

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In this paper, the numerical solution of one-dimensional linear hyperbolic telegraph equation, which describe wave propagation of electric signals in a cable transmission line, is proposed employing the well known homotopy perturbation method(HPM) and laplace transform(LT). Using Laplace transform scheme, the problem is converted into a partial differential equation without any differentiation respect to time. Homotopy perturbation method is applied in the Laplace transform domain. We use Stehfest's numerical inversion algorithm of Laplace transform to retrieve the time domain solution. The performance was found to be very good. The approximate solutions are in excellent agreement with those by the Chebyshev spectral collocation method (CSCM) and the method uses interpolating scaling functions. To illustrate the method some examples are provided. The results show the simplicity and the efficiency of the method.

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Section: Discussionmentioning

confidence: 52%

Section: Numerical Resultsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Telegraph Equation by Using LT Inversion Technique

Javidi

Nyamoradi

2013

International Journal of Advanced Mathematical Sciences

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“…is ( + 1) × ( + 1) tridiagonal matrix,̇is column vector of order ( + 1), and and are ( + 1) order vector, represents the rhs of system (14).…”

Section: Numerical Schemementioning

confidence: 99%

“…Mohebbi and Dehghan [13] reported a higher order compact finite difference approximation of fourth order in space and used collocation method for time direction. Other techniques used for numerical solutions of one-dimensional hyperbolic telegraph equation with Dirichlet boundary conditions are interpolating scaling function technique [14] and radial basis function technique [15]. Thus much work has been done to solve (1) with Dirichlet boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A Collocation Method for Numerical Solution of Hyperbolic Telegraph Equation with Neumann Boundary Conditions

Mittal

Bhatia

2014

International Journal of Computational Mathematics

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We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.

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A computational method for solving two‐dimensional nonlinear variable‐order fractional optimal control problems

Heydari

Avazzadeh

2018

Asian Journal of Control

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In this paper, a new class of two-dimensional nonlinear variable-order fractional optimal control problems (V-OFOCPs) is introduced where the variable-order fractional derivative is defined in the Caputo type. The general procedure for solving theses systems is expanding the state variable and the control variable based on the Legendre cardinal functions in the matrix form. Hence, we derive their operational matrix of derivative (OMD) and operational matrix of variable-order fractional derivative (OMV-OFD). More significantly, some properties of these basis functions are proved to be exploited in our approach. Using these achieved results, we simply expand the matrix form of the nonlinear performance index in terms of the Legendre cardinal functions and subsequently convert it to an algebraic equation. We emphasize that it is a valuable advantage of applying cardinal functions in approximation theory. Then, we implement the OMD and the OMV-OFD of the Legendre cardinal functions to transform the variable-order fractional dynamical system to a system of algebraic equations.Next, the method of constrained extremum is applied to adjoin the constraint equations including the given dynamical system and the initial-boundary conditions to the performance index by a set of undetermined Lagrange multipliers.Finally, the necessary conditions of the optimality are derived as a system of nonlinear algebraic equations including the unknown coefficients of the state variable, the control variable and the Lagrange multipliers. The applicability and efficiency of the proposed approach are investigated through the various types of test problems. KEYWORDS legendre cardinal functions, operational matrix of derivative (OMD), operational matrix of variable-order fractional derivative (OMV-OFD), variable-order fractional optimal control problems

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Numerical solution of telegraph equation using interpolating scaling functions

Cited by 105 publications

References 19 publications

Numerical Solution of Telegraph Equation by Using LT Inversion Technique

Numerical Solution of Telegraph Equation by Using LT Inversion Technique

A Collocation Method for Numerical Solution of Hyperbolic Telegraph Equation with Neumann Boundary Conditions

A computational method for solving two‐dimensional nonlinear variable‐order fractional optimal control problems

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