The modified decomposition method for analytic treatment of differential equations

The modified decomposition method is applied for analytic treatment of nonlinear differential equations. The modified method accelerates the rapid convergence of the series solution, dramatically reduces the size of work, and provides the exact solution by using few iterations only without any need to the so-called Adomian polynomials. Numerical illustrations that include nonlinear PDEs, nonlinear Klein–Gordon equations, and nonlinear Lane–Emden equation, are investigated to show the pertinent features of the technique.