二阶离散方程边值问题的加速单调迭代方法

对一类二阶离散方程边值问题提出了一种加速单调迭代方法,这种方法给出了解的存在比较定理及计算算法,解的单词性改进了解的上解与下解,根据非线性函数的性质迭代具有二阶或几乎二阶的收敛率,数值结果显示了迭代序列的单调收敛性及迭代的收敛率.

Accelerated Monotone Iterative Methods for a Boundary Value Problem of Second-Order Discrete Equation

An accelerated monotone iterative method for a boundary value problem of second-order discrete equation is presented. This method leads to an existence-comparison theorem as well as a computational algorithm for the solutions. The monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration,and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function. Some numerical results are presented to illustrate the monotone convergence of the iterative sequences and the rate of convergence of the iterations.