非线性时滞反应扩散有限差分方程组的高阶单调迭代方法  

Higher-order monotone iterative methods for finite difference systems of nonlinear reaction-diffusion equations with time delays

作　　者：王元明[1,2] 祝明明[1] 

机构地区：[1]华东师范大学数学系,上海200241 [2]上海师范大学,上海高校计算科学E-研究院,"科学计算"上海高校重点实验室,上海200234

出　　处：《应用数学与计算数学学报》2013年第1期40-55,共16页Communication on Applied Mathematics and Computation

基　　金：上海市教育委员会E-研究院建设计划资助项目(E03004);上海市重点学科建设资助项目(B407)

摘　　要：对一类非线性时滞反应扩散方程的有限差分方程组建立了一类高阶单调迭代方法.这类方法给出了一个有效的线性迭代算法.迭代序列单调收敛于方程组的唯一解,并且序列的单调性使得每一步迭代都给出了解的改进的上下界.迭代收敛率具有p+2阶,这里p≥1是一个正整数,它依赖于迭代方法的构造.数值结果显示了方法的有效性.A higher-order monotone iterative method is presented for finite dif- ference systems of a class of nonlinear reaction-diffusion equations with time de- lays. This method leads to an efficient linear iterative algorithm. The sequence of iterations converges monotonically to a unique solution of the system, and the monotonicity property of the sequence gives the improved upper and lower bounds of the solution in each iteration. The rate of convergence of the iterations is of order p ＋ 2, where p≥1 is a positive integer depending on the construction of the iterative method. Numerical results illustrate the effectiveness of the proposed method.

关 键 词：非线性时滞反应扩散方程 有限差分方程组 单调迭代方法 高阶收敛率 

分 类 号：O241.82[理学—计算数学]