A Jacobi collocation approximation for nonlinear coupled viscous Burgers’ equation
ملخص البحث
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- Nyström (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.
الكلمات المفتاحيه
nonlinear coupled viscous Burgers’ equation • Jacobi quadrature rule • pseudospectral scheme • implicit Runge-Kutta-Nyström scheme