一类非线性偏微分方程初边值问题的逐层优化算法

针对非线性偏微分方程初边值问题,基于差分法和动态设计变量优化算法原理,以时间计算层上离散节点的未知函数值为设计变量,以离散节点的差分方程组构造程式化的目标函数,提出了离散节点处未知函数值的逐层高精度优化算法.编制通用程序求解具体典型算例.并通过与解析解对比,表明了求解方法的正确性和有效性,为广泛的工程应用提供条件.

Layered optimization algorithm about a kind of nonlinear partial differential equation with initial-boundary value problem

For non-linear partial differential equations with initial-boundary value problems, based on the difference method and the optimization method with dynamic design variables, using unknown function values on discrete node points on time layer as design variables, the difference equations sets of all the discrete node points are constructed as stylized objective function. A layered accurate optimization algorithm about computing unknown function value on discrete node point is proposed. Universal computing program is designed, and practical examples are analyzed. Through comparing computation results with exact results, the effectiveness and the feasibility of proposed method are verified. The method can provide the condition for engineering application.