Mixed finite element analysis for dissipative SRLW equations with damping term

Two high-precision compact schemes for the dissipative symmetric regular long wave (SRLW) equation by multiple varying bounds integral method

This paper mainly focuses on the numerical study of fourth-order nonlinear dissipative symmetric regular long wave equation. We propose two new methods: the Multiple Varying Bounds Integral (MVBI) method and Taylor Function Fitted (TFF) method. With the multiple varying bounds integral method, all the derivatives in the space direction of the differential equation can be eliminated and we can get different numerical formats by adjusting the integral bound parameters. According to the physical properties of the original differential equation, we can choose an appropriate format from them. Meanwhile, with the Taylor function fitted method, the derivatives of the function at one point, such as first-order and second-order, can be approximated by the original function value at the points around it. Hence, with the MVBI method and TFF method, we can establish two compact and high-precision numerical schemes. In addition, we prove that these numerical schemes are consistent with the original equation on the energy property. Next, the convergence and stability of numerical solution U and P̃ are both proved. Finally, numerical experiments are carried out to verify the effectiveness of numerical schemes.

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 and stability of the schemes are proved by the discrete energy method. Numerical examples are given to support the theoretical analysis.

A decoupled high accuracy linear difference scheme for symmetric regularized long wave equation with damping term

In this paper, the initial boundary value problem of the dissipative symmetric regularized long wave equation with a damping term is studied numerically, and a decoupled linearized difference scheme with a theoretical accuracy of O(?2+h4)is proposed. Because the scheme removes the coupling between the variables in the original equation, the linearized difference scheme and the ex-plicit difference scheme can be used to solve the two variables in parallel, which greatly improves the efficiency of numerical solutions. To obtain the maximum norm estimation of numerical solutions, the mathematical induction and the discrete functional analysis methods are introduced directly to prove the convergence and the stability of the scheme. Numerical experiments have also verified the reliability of the proposed scheme.