A class of new successive permutation iterative algorithms for diffusion equation. Issue 9 (2nd September 2021) - Xu, Qiuyan; Liu, Zhiyong
Abstract : Based on the discretization of full-implicit difference schemes, we construct a new class of successive permutation iterative algorithms for one-dimensional and two-dimensional diffusion equations in this paper. The stability of the new algorithms is guaranteed, and the form of growth matrices are provided in the paper. Compared with the numerical results of the full-implicit difference method, the Gauss–Seidel iterative method and Alternating direction implicit (ADI) method, it is shown that the new algorithms not only have the same accuracy as the full-implicit difference method but also are more accurate and fast than the Gauss–Seidel iterative method and ADI method. Furthermore, the presented algorithms can avoid solving large linear equations, hence improve the calculation speed dramatically.