Extension of the Laplace decomposition method and its application

The Adomian decomposition method was simple and widely used in solving nonlinear differential equations.The convergence region of the Adomian series solution is always very limited.Therefore the Laplace decomposition method,which is a combination of Laplace transformation method and Adomian decomposition method,is proposed to solve initial boundary value problems.In this paper,the Laplace decomposition method is extended to solve nonlinear partial differential equations.For the flaws of the directly extended algorithm,we further proposed a modified algorithm to solve nonlinear partial differential equations.Take,for example,1+1 dimensional nonlinear evolution equation to expound the idea and procedure of the algorithm.Finally,several examples were given to demonstrate the high precision and large convergence region of the new solutions by comparing these new solutions with those Adomian series solutions as well as other known exact solutions.