A Linearized Finite Difference Scheme with Non-uniform Meshes for Semi-linear Parabolic Equation

摘要

In the present paper, a linearized difference scheme with non-uniform meshes for semi-linear parabolic equation is proposed. The scheme is constructed according to the change rule of the solution by travelling wave solution theory for partial differential equation. The existence and uniqueness of the numerical solution are derived by linear systems theory, and the convergence and stability of the difference scheme are proved by the discrete energy method. Numerical simulations verify the theoretical analysis, the results show that the numerical solution with non-uniform meshs is more accurate than that with uniform meshes in the sense of not costing much more computing time. It is concluded that our scheme is effective.