Abstract: The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.
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 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.
Abstract: Based on the homotopy perturbation method (HPM)
and Padé approximants (PA), approximate and exact solutions are
obtained for cubic Boussinesq and modified Boussinesq equations.
The obtained solutions contain solitary waves, rational solutions.
HPM is used for analytic treatment to those equations and PA for
increasing the convergence region of the HPM analytical solution.
The results reveal that the HPM with the enhancement of PA is a
very effective, convenient and quite accurate to such types of partial
differential equations.