To solve the nonlinear finite difference scheme, an accelerated monotone iterative method is presented, and the explicit estimate for the rate of convergence is given.
为了求解非线性差分格式，本文建立一种加速单调迭代算法，并给出精确的收敛率估计。
The method of upper and lower solutions, coupled with the monotone iterative technique is a powerful tool for proving the existence of solutions of nonlinear systems.
单调迭代法与上、下解结合是证明非线性系统解的存在性的强有力的工具。
The numerical results demonstrate the advantages of the method, including the monotone convergence property of iterative sequences and the high accuracy of the method.
数值结果显示了该方法的优越性，包括迭代序列的单调收敛性及有限差分解的高精度。
Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results.
方法应用单调迭代技术结合上下解方法讨论最大解与最小解的存在性。
Upper lower solutions method and monotone iterative technique are applied to initial value problem.
对于初值问题，采用上下解的单调迭代方法求解。
We obtain the existence of extremal solutions of the boundary value problem by using the method of lower and upper solutions coupled with monotone iterative technique.
研究一类四阶微分方程解的存在性，利用上下解及单调迭代的方法，得出这类四阶方程的最大解和最小解的存在。
We obtain the existence of extremal solutions of the boundary value problem by using the method of lower and upper solutions coupled with monotone iterative technique.
研究一类四阶微分方程解的存在性，利用上下解及单调迭代的方法，得出这类四阶方程的最大解和最小解的存在。
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