A generalized collocation method in reproducing kernel space for solving a weakly singular Fredholm integro-differential equations

摘要

A generalized collocation method for solving a weakly singular Fredholm integro-differential equation with Kalman kernel is proposed in reproducing kernel space. To obtain the generalized collocation method, the multiwaves basis in reproducing kernel space W_(n+1) [0, b] is constructed based on Legendre multiwaves in L~2[0,1]. Using the multiwaves basis, we propose ε-approximate solutions and use the method of searching the minimum to obtain the best approximate solution of the equation. Meanwhile, convergence order and stability of the generalized collocation method are studied. It is worth to show that the generalized collocation method proposed in the paper is stable and could be applied to solve other integral equations or differential equations.