Arbitrary Even Order Accuracy Two-Level Explicit Difference Schemes For Parabolic Equations

In this paper,the numerical methods for the initial-boundary problem of the second-order,fourth-order parabolic partial differential equations.The structure of the arbitrary even order accuracy difference scheme is the use of Taylor series expansion method in combination with the second-order and fourth-order partial differential equations themselves,with the increase in accuracy,difference scheme dependent network nodes will be increased,they are a two-level,explicit,and can be calculated from the difference scheme.In this paper,the finite- difference schemes had reasonably extended to the finite- difference schemes of the existing literature.In the calculation, choosing appropriate differential scheme which according to calculating accuracy and computing speed requirements.This article analyzes the stability of difference schemes which use of Fourier method(Von Neumann method),and proves that when r meets certain condition the difference scheme stability.Discussing the algorithm and carrying on the numerical simulation experiments,comparing numerical solutions,exact solutions,and the calculation of the existing literature results,obtaining the second-order,the fourth-order parabolic partial differential equation of arbitrary even order accuracy difference schemes are feasible,effective and in good agreement with the actual calculation.In order to study the numerical methods for the initial-boundary problem of higher-order parabolic partial differential equations providing new methods and new ideas.