New Approximate Method for Systems of Non-linear Volterra Integro-Differential Equations

In this paper, we present a new iterative scheme for approximating nonlinear systems of Volterra-integro-differential equations. The algorithm relies on the principles of the Variational Iteration Method (VIM). The modified method provides successive approximations by variational theory, decomposition techniques, and correction functional on Lagrange’s multiplier. In comparing with numerous results in literatures, which frequently rely on discretization or linearization techniques, this result is of tremendous importance and fewer iterations are enough to obtain a higher degree of accuracy in the solution. We considered three numerical examples to demonstrate the effectiveness and efficiency of the method.