A new numerical scheme for solving systems of integro-differential equations

This paper has been devoted to apply the Reconstruction of Variational Iteration Method (RVIM) to handle the systems of integro-differential equations. RVIM has been induced with Laplace transform from the variational iteration method (VIM) which was developed from the Inokuti method. Actually, RVIM overcome to shortcoming of VIM method to determine the Lagrange multiplier. So that, RVIM method provides rapidly convergent successive approximations to the exact solution. The advantage of the RVIM in comparison with other methods is the simplicity of the computation without any restrictive assumptions. Numerical examples are presented to illustrate the procedure. Comparison with the homotopy perturbation method has also been pointed out.