{"title":"The Comparison of Finite Difference Methods for Radiation Diffusion Equations","authors":"Ren Jian, Yang Shulin","volume":20,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":558,"pagesEnd":561,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/12378","abstract":"In this paper, the difference between the Alternating\r\nDirection Method (ADM) and the Non-Splitting Method (NSM) is\r\ninvestigated, while both methods applied to the simulations for 2-D\r\nmultimaterial radiation diffusion issues. Although the ADM have the\r\nsame accuracy orders with the NSM on the uniform meshes, the\r\naccuracy of ADM will decrease on the distorted meshes or the\r\nboundary of domain. Numerical experiments are carried out to\r\nconfirm the theoretical predication.","references":"[1] P.G. Ciarlet and J.L. Lions, Handbook of Numerical Analysis, Volume I,\r\nFinite Difference Methods (Part 1), Splitting and Alternating Direction\r\nMethods, G.I. Marchuk (North-Holland, 1990).\r\n[2] Deyuan Li, Hongshou Shui, Minjun Tang, On the finite difference scheme\r\nof two-dimensional parabolic equation in a non-rectangular mesh, J.\r\nNumer. Methods Comput. Appl. 4 (1980) 217.\r\n[3] Guangwei Yuan, Zhiqiang Sheng, Analysis of accuracy of a finite volume\r\nscheme for diffusion equations on distorted meshes. J. Comput. Phys.\r\n(2007) 224.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 20, 2008"}