Abstract: Our aim in this piece of work is to demonstrate the
power of the Laplace Adomian decomposition method (LADM) in
approximating the solutions of nonlinear differential equations
governing the two-dimensional viscous flow induced by a shrinking
sheet.
Abstract: In this work we adopt a combination of Laplace
transform and the decomposition method to find numerical solutions
of a system of multi-pantograph equations. The procedure leads to a
rapid convergence of the series to the exact solution after computing a
few terms. The effectiveness of the method is demonstrated in some
examples by obtaining the exact solution and in others by computing
the absolute error which decreases as the number of terms of the series
increases.
Abstract: In this work, we apply the Modified Laplace
decomposition algorithm in finding a numerical solution of Blasius’
boundary layer equation for the flat plate in a uniform stream. The
series solution is found by first applying the Laplace transform to the
differential equation and then decomposing the nonlinear term by the
use of Adomian polynomials. The resulting series, which is exactly the
same as that obtained by Weyl 1942a, was expressed as a rational
function by the use of diagonal padé approximant.