Analytical-approximate solution for nonlinear Volterra integro-dierential equations

In this work, we conduct a comparative study among the combine Laplace trans- form and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro- dierential equations of the second kind. The nonlinear part of integro-dierential is approx- imated by Adomian polynomials, and the equation is reduced to a simple equations. The proper implementation of combine Laplace transform and modied Adomian decomposition method can extremely minimize the size of work if compared to existing traditional tech- niques. Moreover, three particular examples are discussed to show the reliability and the performance of method.