求解一维变系数椭圆型方程边值问题的RBF-FD格式

RBF-FD Scheme for Solving Boundary Value Problems of One-dimensional Elliptic Equations with Variable Coefficients

利用径向基插值函数的Lagrange形式,给出在三等距节点的中心节点处逼近被插函数的有限差分公式及最佳参数值,然后针对一维变系数椭圆型方程建立一种具有四阶精度的RBF-FD差分格式.数值结果表明此差分格式明显优于二阶中心差分格式.

We use Lagrange form of radial basis interpolation function to give the finite difference formula and the optimal parameter values of the interpolated function at the central node of three equidistant nodes. Then,an RBF-FD difference scheme with fourth-order accuracy is established for a one-dimensional variable-coefficient elliptic equation. Numerical results show that the scheme is superior to the second-order central difference scheme.