Finite Difference Methods with intrinsic parallelism For parabolic Equations

摘要

Based on eight saul'yev asymmetry schemes and the concept of domain decomposition, a class of finite difference method (AGE) with intrinsic parallelism for 1D diffusion equations is constructed. Stability analysis for the method is done. We also pay attention to the implementation of the parallel algorithms for 2D convection-diffusion equations. Based on another group of saul'yev asymmetry schemes and the Crank-Nicolson scheme we construct a class of alternating group explicit Crank-Nicolson method(AGEC-N). Both of the present methods are suitable for parallel computation. Stability analysis are also given. In order to verify the methods, we present several numerical examples at the end of the paper. Results of numerical examples show all the methods are of high accuracy.