Research On Uncoupled Linearization Difference Algorithm Of SRLW Equation With Damping Term

Since the two unknown functions u and p in the dissipative SRLW equation with damping term have a coupling relationship,when solving its numerical method,a coupled numerical format is generally established,so the calculation amount is very large,especially for nonlinear ones.The coupled numerical scheme also requires nonlinear iterative solution,which requires more calculations.In this paper,a numerical method for the initial-boundary value problem of a class of dissipative SRLW equations with damping terms is studied by numerical method.The extrapolation technique is used in the numerical discretization.While maintaining the accuracy of the second-order theory,firstly,the coupling term ρx and ux in the equation are simultaneously extrapolated to the n layer and n-1 layer in the time layer,so as to release the coupling relationship between u and ρ in the numerical solution.Then,the nonlinear term uux in the equation is partially extrapolated to the n-1 layer linearized discrete sum two-level linearized discrete in the time layer,thereby establishing three uncoupled three-level linear difference schemes.Since the coupling relationship between the unknown functions u and p in the equation is lifted,only need to solve the functions u and ρ separately in parallel in the numerical solution,and these three formats are all semi-explicit linearized difference formats,in which the numerical solution of the function p is explicit formula algorithm,which greatly improves the efficiency of numerical solution.In the case that the maximum modulus estimate of the difference decomposition cannot be obtained,the discrete functional analysis method and the mathematical induction method are used to directly prove the convergence and unconditional stability of the three schemes,and numerical examples are given.