Some Research About The High Order Finite Difference Scheme For The One-dimensional Extended Fisher-kolmogorov Equation

In this paper, finite difference method is applied to study the one-dimensional Extended Fisher-Kolmogorov equation (EFK). we present three high order finite difference schemes for the problem.The order of the three are allO (ι~2+h~4).The first scheme is a two level nonlinear scheme (S1).Uniqueness, convergence and stability are proved. The second scheme in this paper is a three levellinear difference scheme as Crank-Nicolson. Uniqueness, convergence and stability are also proved.The third scheme is a three level linear scheme(S2) by linearize nonlinear term of the first scheme.Numerical experiments agree with theoretical analysis. Finally, we compare the three differenceschemes from the errors in maximum norm and computing time. S2in computing time is short, S1has high precision.