摘要
WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between third order and fourth order, and fourth-order accuracy is achieved in the case of the same grid steps being used within the computational domain. Two numerical examples are given to demonst ate the advantages of the proposed scheme. Compared with the conventional difference scheme, more accurate numerical solution can be obtained by using the proposed scheme even with relatively larger grid sizes. It is also pointed out that the appropriate structure of the nonuniform grid can not only make the proposed scheme more practical, but lead to a solution superior to that for a uniform grid structure. [WT5”HZ]
WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between third order and fourth order, and fourth-order accuracy is achieved in the case of the same grid steps being used within the computational domain. Two numerical examples are given to demonst ate the advantages of the proposed scheme. Compared with the conventional difference scheme, more accurate numerical solution can be obtained by using the proposed scheme even with relatively larger grid sizes. It is also pointed out that the appropriate structure of the nonuniform grid can not only make the proposed scheme more practical, but lead to a solution superior to that for a uniform grid structure. [WT5”HZ]
基金
ProjectsupportedbytheMajorStateBasicResearchDevelopmentProgram (No .G19990 436 )andthe"Trans CenturyTrainingProgramFoundationfo
