Numerical analysis of an uncoupled and linearized compact difference scheme with energy dissipation property for the generalized dissipative symmetric regularized long-wave equations

This paper proposes and analyzes an uncoupled and linearized compact finite difference scheme for the generalized dissipative symmetric regularized long-wave (GDSRLW) equations. The unique solvability and some a priori estimates of the proposed difference scheme are rigorously proved based on the mathematical induction method. To obtain the ||center dot||infinity$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$-norm estimation of numerical solutions, the discrete energy method is used to prove the convergence and stability of the difference scheme. The proposed difference scheme preserves the original energy dissipation property, and the convergence of the scheme is proved to be fourth-order in space and second-order in time in the ||center dot||infinity$$ {\left\Vert \cdotp \right\Vert}_{\infty } $$-norm for both u$$ u $$ and rho$$ \rho $$. Some numerical experiments are given to verify the theoretical analysis and the reliability of the proposed difference scheme.