Numerical solution of initial-boundary system of nonlinear hyperbolic equations

E. H. Doha (), A. H. Bhrawy (), M. A. Abdelkawy () and R. M. Hafez ()
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E. H. Doha: Cairo University
A. H. Bhrawy: King Abdulaziz University
M. A. Abdelkawy: Beni-Suef University
R. M. Hafez: Modern Academy

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 5, 647-668

Abstract: Abstract In this article, we present a numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral Jacobi-Gauss-Radau collocation (J-GR-C) method. A J-GR-C method in combination with the implicit Runge-Kutta scheme are employed to obtain a highly accurate approximation to the mentioned problem. J-GR-C method, based on Jacobi polynomials and Gauss-Radau quadrature integration, reduces solving the system of nonlinear hyperbolic equations to solve a system of nonlinear ordinary differential equations (SNODEs). In the examples given, numerical results by the J-GR-C method are compared with the exact solutions. In fact, by selecting relatively few J-GR-C points, we are able to get very accurate approximations. In this way, the results show that this method has a good accuracy and efficiency for solving coupled partial differential equations.

Keywords: System of nonlinear hyperbolic equations; collocation method; Jacobi-Gauss-Radau; quadrature; implicit Runge-Kutta method (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0152-5

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