analytical-approximate solution for nonlinear volterra integro-differential equations

In this work, we conduct a comparative study among the combine laplace transform and modified adomian decomposition method (lmadm) and two traditional methods for an analytic and approximate treatment of special type of nonlinear volterra integrodifferential equations of the second kind. the nonlinear part of integro-differential is approximated by adomian polynomials, and the equation is reduced to a simple equations. the proper implementation of combine laplace transform and modified adomian decomposition method can extremely minimize the size of work if compared to existing traditional techniques. moreover, three particular examples are discussed to show the reliability and the performance of method.