用径向基函数解一类微积分方程

通过一个数值算例，探讨了用径向基函数解一类微积分方程的问题。针对数值算例，比较了在相同步长时，不同的径向基函数对微积分方程数值解的精确程度，并比较不同的正定径向基函数在相同的形状参数时绝对误差的差异，说明径向基函数形状参数的选取与方程数值解的精度密切相关，同时也论证了在插值过程中所得到的矩阵方程解的存在唯一性。

Using radial basis function to solve an integral -differential equation

An algorithm for integral -differential equation based on the positive definite radial basis tunction approximation scheme is presented. A fairly explicit scheme is used to approximate the solution. One model problem of the algorithm is given. The comparison is made with the exact solutions of the problem by different shape parameter and different nodal distance, illustrating that numerical results may not be better when nodal distance is smaller. The shape parameter of radial basis functions is important for the numerical solution of Integral- differential Equation. This paper proved that the coefficient matrix that we obtained is nonsingular, that is, matrix equation has a solution.