A collocation approach for solving two-dimensional second-order linear hyperbolic equations
APPLIED MATHEMATICS AND COMPUTATION, vol.338, pp.101-114, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 338
- Publication Date: 2018
- Doi Number: 10.1016/j.amc.2018.05.053
- Journal Name: APPLIED MATHEMATICS AND COMPUTATION
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.101-114
- Keywords: Two-dimensional hyperbolic telegraph equations, Partial differential equations, Bessel functions of first kind, Collocation method, Collocation points, Numerical solutions, TELEGRAPH EQUATION, NUMERICAL-SOLUTION, INTERPOLATION, DIRICHLET, SCHEME
- Akdeniz University Affiliated: Yes
Abstract
In this study, a collocation approach is introduced to solve second-order two-dimensional hyperbolic telegraph equation under the initial and boundary conditions. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. The method is constructed in four steps for the considered problem. In first step we construct the fundamental relations for the solution method. By using the collocation points and matrix operations, second step gives the constructing of the main matrix equation. In third step, matrix forms are created for the initial and boundary conditions. We compute the approximate solutions by combining second and third steps. Algorithm of the proposed method is given. Later, error estimation technique is presented and the approximate solutions are improved. Numerical applications are included to demonstrate the validity and applicability of the presented method. (C) 2018 Elsevier Inc. All rights reserved.