The Explicit Difference scheme for One-dimensional Nonlinear Coupled Wave Equations

In this paper, the explicit difference scheme is used to numerically calculate the one-dimensional nonlinear coupled wave equations, and the energy analysis method is used to analyze the convergence. It is proved that it has a convergence order of O\left( \tau ^2 + h^2 \right) in maximum norm. Using Richardson extrapolation method, extrapolation solutions with an order of O\left( \tau ^4 + h^4 \right) in L^\infty -norm are obtained. Finally, numerical results confirm numerical solutions obtained by our explicit difference scheme are convergent with an order of two in both time and space; this method own some advantages, such as, low time cost, simple implementation. Our findings possess guiding significance for the development and theoretical analyses of high-performance algorithms used to solve nonlinear coupled wave equations.