Septic B-Spline Collocation Method For Solving One-Dimensional Hyperbolic Telegraph Equation

Dosti, Marzieh; Nazemi, Alireza

doi:10.5281/zenodo.1331893

Cited by 4 publications

References 23 publications

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Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

Mittal

Bhatia

2014

2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

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This paper, presents a relatively new approach to solve second order one dimensional non-linear wave equation. We use modified cubic B-spline basis functions based differential quadrature method for space discretization, which gives results in an amenable system of differential equations. The resulting system of equations has been solved using SSP-RK43 scheme. The SSP-RK43 scheme needs less storage space and causes less accumulation of numerical errors. The utility of the scheme is that it does not need any linearization or transformation for handling the non-linear terms and hence reduces the computational effort. The accuracy of the approach has been confirmed with numerical experiments. 2 and ∞ error norms are computed for each example and it is shown that the results obtained are acceptable and are in good agreement with the earlier studies.Keywords-Non-linear wave equations, Modified cubic B-spline basis functions, Differential quadrature method, Thomas algorithm.

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Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

Mittal

Bhatia

2014

2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI)

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An efficient algorithm based on the multi-wavelet Galerkin method for telegraph equation

Jebreen¹,

Chalco-Cano²,

Dassios

2021

AIMS Mathematics

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A novel B-spline collocation method for Hyperbolic Telegraph equation

Kirli

2023

MATH

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<abstract><p>The present study is concerned with the construction of a new high-order technique to establish approximate solutions of the Telegraph equation (TE). In this technique, a novel optimal B-spline collocation method based on quintic B-spline (QBS) basis functions is constructed to discretize the spatial domain and fourth-order implicit method is derived for time integration. Test problems are considered to verify the theoretical results and to demonstrate the applicability of the suggested technique. The error norm $ L_{\infty } $ and the rate of spatial and temporal convergence are computed and compared with those of techniques available in the literature. The obtained results show the improvement and efficiency of the proposed scheme over the existing ones. Also, it is obviously observed that the experimental rate of convergence is almost compatible with the theoretical rate of convergence.</p></abstract>

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Septic B-Spline Collocation Method For Solving One-Dimensional Hyperbolic Telegraph Equation

Cited by 4 publications

References 23 publications

Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

Numerical solution of some nonlinear wave equations using modified cubic B-spline differential quadrature method

An efficient algorithm based on the multi-wavelet Galerkin method for telegraph equation

A novel B-spline collocation method for Hyperbolic Telegraph equation

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