A New Technique for Solving a Class of Nonlinear Initial-Boundary Value Problems

In this paper, a new technique for solving a class of Nonlinear Initial-Boundary Value Problems (NIBVPs) is introduced. The main advantage of this technique is that it utilizes both initial and boundary conditions in the Adomian series solution and consequently, an accurate approximate solution is obtained in both temporal and spatial directions. The sufficient condition that guarantees a unique solution is obtained. Convergence of the series solution is proved and the truncated error is estimated. Some numerical examples are discussed to illustrate the effectiveness of the proposed technique.