一类具有非线性边界条件的四阶方程的紧差分迭代解法  

ITERATIVE COMPACT DIFFERENCE SCHEME FOR A FOURTH-ORDER EQUATION WITH NONLINEAR BOUNDARY CONDITION

作　　者：庄清渠[1] 任全伟[2] 

机构地区：[1]华侨大学数学科学学院,泉州362021 [2]上海师范大学数理学院,上海200234

出　　处：《高等学校计算数学学报》2016年第4期289-300,共12页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(No.11501224);华侨大学中青年教师科研提升资助计划项目(No.ZQN-PY201)

摘　　要：科学和工程计算中许多问题的数学模型都可用四阶微分方程来表述．如刻画火焰传播的Kuramoto—Sivashinsky方程以及描述固体复杂的相位分离以及粗化现象的Cahn—Hilliard方程[1，2，3]．而在应用惩罚法于带有边界约束的四阶变分不等式时则会产生带非线性边界条件的四阶方程[4]．A compact difference scheme is proposed to solve a class of fourth-order differential equation with nonlinear boundary condition. Rigorous error analysis of the scheme is carried out. Newton iterative method and difference quotient iterative method are presented to deal with the nonlinear boundary problem respectively. Numerical results show that the approximation scheme is effective and the accuracy of the scheme is of O（h4）.

关 键 词：非线性边界条件 四阶方程 迭代解法 差分 四阶微分方程 变分不等式 相位分离 火焰传播 

分 类 号：O241.82[理学—计算数学]