一类非线性高阶退化拟抛物方程的有限差分方法  

Finite Difference Method for A Class of Nonlinear High Order Degenerate Quasi-Parabolic Equations

作　　者：李清纯 张继红[1] 梁波[1] LI Qingchun;ZHANG Jihong;LIANG Bo(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》2021年第4期118-120,共3页Journal of Dalian Jiaotong University

基　　金：国家自然科学基金青年科学基金资助项目(11801056);辽宁省教育厅自然科学青年基金资助项目(JDL2019034)。

摘　　要：研究了一类高阶退化拟抛物方程的有限差分算法,所研究的方程中含有粘性松弛因子以及P-双调和算子.在假定一些初值的情况下,利用差商分别对p=2,p=3时的两个方程中各项的时间和空间导数项进行离散化,采用中心差分法以及向前欧拉法构造出了非线性偏微分方程的差分格式。最后针对具体方程进行了数值实验,并利用Matlab软件比较和分析了数值解与真实解之间的误差,验证了有限差分法对此方程的数值求解的可行性.The finite difference method for a class of nonlinear high-order degenerate quasi parabolic equations with viscous relaxation factor and p-biharmonic operator is studied.Assuming some initial values,the difference quotients are used to approximate the temporal and spatial differential terms in the two equations wherep=2 andp=3 respectively.The central difference and the forward difference can be applied to obtain the difference equations.Finally,numerical experiments are carried out for the specific example,and the errors between the numerical solutions and accurate solutions are compared and analyzed by MATLAB software.The experiment results show that the method is effective.

关 键 词：化拟抛物方程 粘性松弛因子 有限差分法 高阶方程 

分 类 号：O241.82[理学—计算数学]