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 nonlinear 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 \mathcal{O}(h^{\min\{\frac{۷}{۲}, q-\frac{۱}{۲}\}}). Ample numerical results are addressed to confirm the expected convergence order as well as the accuracy and efficiency of the proposed method.

کلیدواژه ها:

Nonlinear Fredholm integro-differential equations ، singular two-point boundary value ، Numerical Method