圆锥型径向基函数的配点法及其应用

Collocation Points for the Conical Radial Basis Function Method and their Application

针对拉普拉斯控制方程边值问题的数学模型,用圆锥型径向基函数配点法进行数值模拟.用切比雪夫节点作为数值模拟过程中的配点,与传统圆锥型径向基函数配点法和解析解的结果进行了对比,数值结果表明:利用切比雪夫节点的圆锥型径向基函数配点法模拟椭圆型偏微分方程边值问题达到更好的结果,为其理论研究奠定基础.

Based on the elliptic partial differential equations,the conical radial basis function method was investigated.During the solution process,Chebyshev points,combined with the conical radial basis function method,were introduced.Numerical results,which were compared with the traditional conical radial basis function method as well as with analytical solutions,show that the improved conical radial basis function method—a foundation for the theoretical research—is superior to the traditional Kansa’s method in terms of solution accuracy and boundary improvement.