四阶常微分方程的Birkhoff配点法  

Birkhoff Collocation Method for Fourth-Order Ordinary Differential Equations

作　　者：庄清渠[1] 王金平[1] ZHUANG Qingqu;WANG Jinping(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2018年第2期306-311,共6页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11501224);华侨大学中青年教师科研提升资助计划项目(ZQN-PY201)

摘　　要：提出求解四阶常微分方程的Birkhoff配点法.通过构造满足边界条件的Birkhoff插值基函数,得到具有稳定条件数的代数方程组.在数值算例中,通过与一类Legendre配点法的数值结果进行比较.结果表明:Birkhoff配点法的有效性和高精度.The paper presents a Birkhoff collocation method for solving the fourth order differential equation.The Birkhoff interpolation basis functions satisfying the boundary conditions are constructed,which leads to algebraic equations with stable condition numbers.Numerical results indicate that the Birkhoff collocation method is of high accuracy and effectiveness comparing with a kind of Legendre collocation method.

关 键 词：四阶常微分方程 Birkhoff配点法 Legendre配点法 代数方程组 

分 类 号：O241.8[理学—计算数学]