Information Technology Journal1812-56381812-5646Asian Network for Scientific Information10.3923/itj.2010.1184.1189JinYuanfeng JinGuangzhi MaTinghuai 6201096To solve the diffusion equation on parallel computers, we first derived an o(τ^{2}+h^{6}) order implicit finite difference method based on a class of alternating group explicit iterative method. Based on this method, we devised a new alternating group explicit iterative method. Moreover, the absolute stability and convergence of the New Alternating Group Explicit Iterative (N-AGEI) method was proved. Finally, the numerical experiments were conducted to verify our method. Both the theoretical analysis and simulation results showed that our proposed difference format had satisfied stability error estimate and convergence.]]>Dawson, C.N. and T.F. Dupont,1992Evans. D.J. and A.R.B. Abdullah,1983Evans, D.J. and A.R.B. Abdullah,19832u/∂x^{2}+∂^{2}u/∂y^{2}.]]>Evans, D.J.,1985Evans. D.J. and M.S. Sahimi,1988Tavakoli, R. and P. Davami,2006Tavakoli, R. and P. Davami,2006Yuan, G.W., L.J. Shen and Y.L. Zhou,2001Zheng, B.,2009Zhang, B.L. and G.X. Yuan,1994Zhang, B.L. and L.J. Shen,1995Jin, Y.,2010