A Chebyshev-Gauss-Radau Scheme For Nonlinear Hyperbolic System Of First Order

Research Abstract

A numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral collocation method is presented in this article. A Chebyshev-Gauss-Radau collocation (C-GR-C) method in combination with the implicit Runge- Kutta scheme are employed to obtain highly accurate approximations to the mentioned problem. The collocation points are the Chebyshev interpolation nodes. This approach reduces this problem to solve system of nonlinear ordinary differential equations which are far easier to be solved. Indeed, by selecting a limited number of collocation nodes, we obtain an accurate results. The numerical examples demonstrate the accuracy, efficiency, and versatility of the method.

Research Keywords

System of nonlinear hyperbolic equations; Collocation method; Chebyshev-Gauss-Radau quadrature; Implicit Runge- Kutta method