摘要
针对高阶非线性动力学问题的求解,提出了一种改进的有限点集法(corrected finite pointset method,CFPM).首先将具有高阶导数的非线性偏微分方程分解为若干一阶偏微分方程,并采用有限点集法对其进行离散求解;然后连续应用低阶导数逐阶逼近高阶导数;最后对比一维非线性黏性Burgers方程及具有高阶导数的Kd V-Burgers方程的数值解与解析解,并将二维非线性Burgers方程的数值结果与其他数值结果进行比较.实例分析表明,CFPM方法能够准确、可靠地求解非线性动力学问题.
A corrected finite point-set method（CFPM）is proposed to solve the non-linear dynamics problems in this paper.The improvements in the proposed method are：the high-order partial differentiable equation（PDE）is decomposed into multi-first-order PDE;the obtained first-order PDE is discretized using the finite point-set method（FPM）;the discretization scheme of first-order PDE is continuously used to solve the higher-order PDE.To test the ability and merits of the proposed CFPM,one-dimensional（1D）Burgers equation with analytical solutions,1DKdV-Burgers equation with three-order derivatives and 2D Burgers equation with initial boundary values condition are solved in turn,and compared with the analytical or other numerical solutions.The numerical results show that the CFPM can accurately and reliably solve the non-linear dynamics problems.
出处
《扬州大学学报（自然科学版）》
CAS
北大核心
2015年第3期20-23,36,共5页
Journal of Yangzhou University：Natural Science Edition
基金
国家自然科学基金资助项目(51309200)
江苏省自然科学基金资助项目(BK20130436)
中国博士后科学基金面上资助项目(2014M550310)
