$$L^{\infty }$$ L ∞ error bound of conservative compact difference scheme for the generalized symmetric regularized long-wave (GSRLW) equations

Abstract

In this paper, we design a compact finite difference scheme which preserves the original conservative properties to solve the generalized symmetric regularized long-wave equations. The existence of the difference solution is proved by the Brouwer fixed-point theorem. Applying the discrete energy method, the convergence and stability of the difference scheme is obtained, and its numerical convergence order is $$O(\tau ^{2}+h^{4})$$ in the $$L^{\infty }$$ -norm for u and $$\rho $$ . For computing the nonlinear algebraic system generated by the compact scheme, a decoupled iterative algorithm is constructed and proved to be convergent. Numerical experiment results show that the theory is accurate and the method is efficient and reliable.