The modified decomposition method for analytic treatment of non-linear integral equations and systems of non-linear integral equations

We demonstrate the use of the modified decomposition method for the analytic treatment of non-linear Fredholm integral equations, non-linear Volterra integral equations and systems of non-linear integral equations. The proper implementation of the modified method can dramatically reduce the amount of work required and may provide the exact solution using only a few iterations. The analysis is accompanied by numerical illustrations that show the pertinent features of the technique.