New Tchebyshev-Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations. (English) Zbl 1355.65129
A. Saadatmandi and M. Dehghan [Numer. Methods Partial Differ. Equations 26, No. 1, 239–252 (2010; Zbl 1186.65136)] have used the operational matrices to solve hyperbolic telegraph type equations. In this article appropriate basis functions are constructed and their operational matrices of differentiation and integration are developed, which along with applications of Galerkin and collocation methods are used in order to solve linear and nonlinear second-order hyperbolic telegraph type equations subject to initial, homogeneous/nonhomogeneous boundary conditions. Numerical examples are given to illustrate applications and the high accuracy of the two algorithms introduced here.
Reviewer: H. P. Dikshit (Bhopal)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 35L70 | Second-order nonlinear hyperbolic equations |
Keywords:
Chebyshev polynomials; Galerkin method; collocation method; hyperbolic telegraph equation; operational matrix; numerical examplesCitations:
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