A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

作者：Doha Eid H; Bhrawy Ali H; Abdelkawy Mohamed A^*; Hafez Ramy M

来源：Central European Journal of Physics, 2014, 12(2): 111-122.

DOI：10.2478/s11534-014-0429-z

• nonlinear coupled viscous Burgers' equation
• Jacobi quadrature rule
• pseudospectral scheme
• implicit Runge-Kutta-Nystrom scheme

This 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.

• 出版日期2014-2