A Laplace Adomian Decomposition Approximation Solution For Boundary Layer Equations

In this work, we apply the Laplace Adomian decomposition method to find series solutions ofthe nonlinear differential equations governing boundary layer flows.The Laplace Adomian decomposition method is a very powerful tool for solving linear andnonlinear differential equations. The basic technique of this method is a combination of theLaplace transforms method and the Adomian decomposition algorithm. It assumes that thesolution of a nonlinear differential equation can be expressed as a power series in which thenonlinear terms are decomposed by the use of Adomian polynomials. Since Laplacetransformation requires that boundary conditions be given, we start by assuming their existence,in cases in which they are not given, and later determine them from the resulting series solutionby the use of Pade approximants or the method of steepest decent.To demonstrate its effectiveness and convergence, the method is first tested on somedifferential equations and the results obtained compared with the exact solutions or thoseobtained by alternative procedure. Comparison indicates that our method is quite accurate,reliable and the series converges rapidly to the exact solution.