Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic B-spline collocation method

Mittal, R. C.; Bhatia, Rachna

doi:10.1016/j.amc.2013.05.081

Cited by 58 publications

(86 citation statements)

References 17 publications

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“…We have used the following modified form of cubic B-spline basis functions [21] in the combination with collocation, to solve the sine-Gordon equation. Modified cubic B-spline basis functions have been used for handling the Dirichlet boundary conditions and finally we obtain a diagonally dominant system of differential equations.…”

Section: Numerical Schemementioning

confidence: 99%

Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

Mittal

Bhatia

2014

International Journal of Partial Differential Equations

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Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies.

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Section: Numerical Schemementioning

confidence: 99%

Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

Mittal

Bhatia

2014

International Journal of Partial Differential Equations

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“…Hesameddini and Asadolahifard [17] applied the Sinc-Collocation Method to approximate the solution of (1). Mittal and Bhatia [18] and Rashidinia et al [19] employed the Cubic B-spline Collocation Method (CuBSCM) to approximate the solution of (1). In [20], the authors employed the Fibonacci Polynomials approach to approximate solution of telegraph equations.…”

Section: Introductionmentioning

confidence: 99%

Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation

Adewumi

Akindeinde

Aderogba

et al. 2017

International Journal of Engineering Mathematics

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This article presents a new numerical scheme to approximate the solution of one-dimensional telegraph equations. With the use of Laplace transform technique, a new form of trial function from the original equation is obtained. The unknown coefficients in the trial functions are determined using collocation method. The efficiency of the new scheme is demonstrated with examples and the approximations are in excellent agreement with the analytical solutions. This method produced better approximations than the ones produced with the standard weighted residual methods.

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“…In the literature the -spline collocation method has been successfully applied to find the numerical solutions of various linear and nonlinear partial differential equations [6,18,19].…”

Section: Introductionmentioning

confidence: 99%

“…In [4], H.-W. Liu and L.-B. Liu applied an unconditionally stable spline difference method; Dosti and Nazemi [5] presented a quartic -spline collocation method; modified cubic -spline collocation method has been proposed by Mittal and Bhatia [6] to find the numerical solution of one-dimensional linear hyperbolic telegraph equation. Numerical solution of linear and nonlinear onedimensional hyperbolic telegraph equation with variable coefficient has been presented in [7,8].…”

Section: Introductionmentioning

confidence: 99%

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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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Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic B-spline collocation method

Cited by 58 publications

References 17 publications

Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method

Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation

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

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