Research On The Linear Difference Method Of BBM Equation

Since the linear difference scheme does not need iteration in the process of numerical calculation and the calculation time is relatively saved,it is a significant work in the field of numerical research to construct a high-precision linearized difference scheme.In this paper,the finite difference method for the initial boundary value problem of a class of BBM equations with nonlinear diffusion and dissipation terms is studied.Firstly,BBM equation is linearized and discretized,and the nonlinear termuu_x is extrapolated to the n-1 layer in the time layer,a three-layer linear difference scheme withO??²?10?h²?theoretical accuracy is proposed.Then use Richardson extrapolation of ideas in the space for extrapolation,make the space layer has the theory of fourth order accuracy,so as to construct aO??²?10?h⁴?theoretical accuracy of three layers of linear difference format,at can't get the difference of maximum modulus to estimate,the integrated use of mathematical induction and discrete functional analysis methods,directly prove the convergence and stability of the two formats.In literature^[36]to BBM equation with second order theory put forward by the precision of the three layers of average implicit difference scheme?linear?in the space layer Richardson extrapolation,a three-layer average implicit difference scheme withO??²?10?h⁴?theoretical accuracy of fourth order is proposed for BBM equations,one of the conserved quantities is reasonably simulated,the priori estimation and existence uniqueness of its difference decomposition are discussed,and analyses its convergence and stability.Finally,numerical examples show that the three linear difference schemes proposed for BBM equation are effective and reliable.