四阶常微分方程的Birkhoff配点法

Birkhoff Collocation Method for Fourth-Order Ordinary Differential Equations

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.