一类非线性反应扩散方程的数值解法 - 昆明理工大学学报.PDF

34 5 () http: / /www. kustjourna.l com/ V o.l 34 N o5 2009 10 Journal ofK unm ing U n iversity of Science and T echnology ( Science and T echnology Oct. 2009 do:i 10. 3969 / j. issn. 1007- 855x. 2009. 05. 025 舒阿秀, 胡万宝 ( , 24 60 11 : 建立了一个用于求解一类非线性反应扩散方程的有限差分方法, 在空间和时间方向 该 方法分别具有四阶和二阶精度 建立了一个单调迭代算法用于求解非线性格式, 讨论了数值解 的收敛性 : 非线性反应扩散方程; 有限差分方法; 单调迭代 : O24182 : A : 1007- 855X ( 2009 05- 0112- 04 NumericalM ethods for a Class ofReaction- Diffusion Equation SHU Ax iu, HU W anbao ( D epartm ent o f M athem atics, A nqing N orm a l College, A nqing, A nhui 246011, China bstract: A finite difference m ethod to so lve non linear reaction- diffu sion equations is proposed in th is paper, w hich has accuracies o f fourth order in space and second order in t mi e. A m onotone iterat ive schem e is deve l oped to so lve the nonlinear d iscrete schem e. The convergence of the d iscrete schem e is also discu ssed. Key words: non linear reaction- diffu sion equations; f inite d ifference schem e; m onotone iteration 0 [ 1- 6] , , , [ 3- 4] , ( [ 5- 6] . [ 6] , . : 2 u u n = 2 + u ( 1 - u), a x b, 0 t T t x ( 1) u ( a, t) = u0 ( t), u ( b, t) = u1 ( t), 0 t T u (x, 0) = u0 (x ), a x b u u (x, t) t, 1, 2u(), t () , n =