Doha, EHBhrawy, A. H.Abdelkawy, M. A.Hafez, R. M.2019-11-202019-11-2020150019-5588https://doi.org/10.1007/s13226-015-0152-5https://insa.nic.in/UI/Searchlisting.aspx?kwd=Numerical%20solution%20of%20initial-Accession Number: WOS:000362666400004In 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.enUniversity of System of nonlinear hyperbolic equationsCollocation methodJacobi-Gauss-Radau quadratureImplicit Runge-Kutta methodRESOLUTIONSPECTRAL-COLLOCATION METHODVOLTERRA INTEGRAL-EQUATIONSArticlehttps://doi.org/10.1007/s13226-015-0152-5