非线性偏微分方程边值问题的优化算法研究与应用  

Study and application of optimization algorithm about nonlinear partial differential equations with boundary value problem

作　　者：侯祥林[1] 刘铁林[2] 翟中海[1] 

机构地区：[1]沈阳建筑大学理学院,沈阳110168 [2]沈阳建筑大学土木工程学院,沈阳110168

出　　处：《物理学报》2011年第9期13-21,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号10972144);辽宁省自然科学基金(批准号20072011);辽宁省教育厅项目(批准号:L2010445)资助的课题~~

摘　　要：针对椭圆类非线性偏微分方程边值问题,以差分法和动态设计变量优化算法为基础,以离散网格点未知函数值为设计变量,以离散网格点的差分方程组构建为复杂程式化形式的目标函数.提出一种求解离散网格点处未知函数值的优化算法.编制了求解未知离散点函数值的通用程序.求解了具体算例.通过与解析解对比,表明了本文提出求解算法的有效性和精确性,将为更复杂工程问题分析提供良好的解决方法.For elliptic nonlinear partial differential equations with boundary value problem, based on difference method and dynamic design variable optimization method, by taking unknown function value on discrete net point as design variables, difference equation of all the discrete net points is constructed as an objective function. A kind of optimization algorithm about solving unknown function value on discrete net point is proposed. Universal computing program is designed. Practical example is analyzed. By comparing the computing result with the analytical solution, effectiveness and feasibility are verified. Thus complicated nonlinear mathematical physics equations can be solved by the numerical calculation method.

关 键 词：非线性偏微分方程 边值问题 动态设计变量优化算法 程序设计 

分 类 号：O175.8[理学—数学]