Fully discretized methods based on boundary value methods for solving diffusion equations

Based on boundary value methods, we establish a kind of new fully discretized methods for solving one-dimensional diffusion equations. The proposed methods are composed of a series of full discretizations with multi-time-level and multi-space-level. For the full discretizations, we give the local truncation error. Moreover, we analyze the stability of the proposed methods and obtain the corresponding error estimate. Meanwhile, we make some numerical experiments to show that the proposed methods are stable and own high accuracy.