Doha, Eid H.Bhrawy, Ali H.Abdelkawy, Mohamed A.Hafez, Ramy M.2019-12-042019-12-042014Cited References in Web of Science Core Collection: 381895-1082https://doi.org/10.2478/s11534-014-0429-zhttps://cyberleninka.org/article/n/1095471/viewerAccession Number: WOS:000331705700005This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nystrom (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.enUniversity for nonlinear coupled viscous Burgers' equationpseudospectral schemeimplicit Runge-Kutta-Nystrom schemeDIFFERENTIAL-EQUATIONSINTEGRAL-EQUATIONSNUMERICAL-SOLUTIONMODELArticlehttps://doi.org/10.2478/s11534-014-0429-z