一类非线性四阶偏微分方程的数值结果  

Numerical Results for A Nonlinear Fourth-Order Partial Differential Equation

作　　者：梁波[1] 王洁欣 李永菲 张继红[1] 汪颖[1] LIANG Bo;WANG Jiexin;LI Yongfei;ZHANG Jihong;WANG Ying(School of Science,Dalian Jiaotong University,Dalian 116028,China)

机构地区：[1]大连交通大学理学院,辽宁大连116028

出　　处：《大连交通大学学报》2020年第2期118-120,共3页Journal of Dalian Jiaotong University

基　　金：国家自然科学基金资助项目(11801056);辽宁省自然科学基金资助项目(20170540136);辽宁省博士启动基金指导计划资助项目(20170520431)。

摘　　要：研究了一类非线性四阶偏微分方程解的数值结果.所研究问题的最高阶部分为四阶线性微分项,低阶部分为二阶非线性微分项.在初边值条件下,用有限差分法对方程的各项进行离散,用向后欧拉法及中心差分法构造出方程的显示形式.最后给出实例,选取恰当的拟合函数,赋予方程一定的初始边界条件,并用Matlab软件对结果进行检验,得到较高的精确效果.The numerical results of solutions for a class of nonlinear fourth-order partial differential equations are studied.For the form of the problem,the highest-order term is given by a fourth-order linear differential,and the second-order term is given by a second-order nonlinear differential.The finite difference method is used to discretize the equations with some initial boundary conditions.The backward Euler method and the central difference method are used to construct the explicit form of the equation.Finally,an example is given by an appropriate fitting function with some initial boundary conditions.The results are checked by Matlab software and some accurate results are obtain.

关 键 词：四阶偏微分方程 BCF模型 有限差分法 MATLAB 

分 类 号：O241.82[理学—计算数学]