NUMERICAL TREATMENT OF COUPLED NONLINEAR HYPERBOLIC KLEIN-GORDON EQUATIONS

作者：Doha E H^*; Bhrawy A H; Baleanu D; Abdelkawy M A

来源：Romanian Journal of Physics, 2014, 59(3-4): 247-264.

• Nonlinear coupled hyperbolic Klein-Gordon equations
• Nonlinear phenomena
• Jacobi collocation method
• Jacobi-Gauss-Lobatto quadrature

A semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.

• 出版日期2014