effective numerical methods for nonlinear singular two-point boundary value fredholm integro-differential equations

We deal with some effective numerical methods for solving a class of nonlinear singular two-point boundary value fredholm integro-differential equations. using an appropriate interpolation and a q-order quadrature rule of integration, the original problem will be approximated by the non-linear finite difference equations and so reduced to a nonlinear algebraic system that can be simply implemented. the convergence properties of the proposed method are discussed, and it is proved that its convergence order will be of o(hmin{ 7/2 ,q− 1/2 }). ample numerical results are addressed to con-firm the expected convergence order as well as the accuracy and efficiency of the proposed method.