Coupled and decoupled high-order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations

In this paper, two coupled and decoupled dissipative finite difference schemes with high-order accuracy are proposed for solving the dissipative generalized symmetric regularized long wave equations. Dissipation of the discrete energy of scheme with different parameters is discussed. A priori estimate, existence and uniqueness of numerical solutions, convergence with O(tau 2+h4) and stability of the schemes are proved by the discrete energy method. Numerical examples are given to support the theoretical analysis.

Automated summary

Two coupled and decoupled dissipative finite difference schemes with high-order accuracy are proposed for solving the dissipative generalized symmetric regularized long wave equations in this paper. Dissipation of the discrete energy with different parameters is discussed, and the a priori estimate, existence and uniqueness of numerical solutions, convergence with O(tau 2+h4), and stability of the schemes are proved by the discrete energy method. Numerical examples are provided to support the theoretical analysis.