A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel

Abstract

A stable least residue method for solving a nonlinear fractional integro-differential equation with a weakly singular kernel in the reproducing kernel space is proposed. To solve the equation, the multiwavelets bases in the reproducing kernel space are constructed based on the cubic Legendre wavelets in L2[0,1]. The best approximate solution could be obtained by solving the normal equation. Meanwhile, we provide the adaptive convergence order and the stability proof of the scheme. It is encouraging that the new method is stable and the accuracy of the method is preserved even in the case if the solution has fast oscillations. Four examples strongly demonstrate the validity of the scheme.