Abstract Most of the real-life problems experienced in industry these days cannot be expressed as a single differential equation but system equations. Such structures linear partial models are considered this work with aid Laplace Adomian decomposition method (LADM) terms solutions. Various examples taken into consideration. The results easily obtained, good agreement when compared to their exa...

To solve the weakly-singular Volterra integro-differential equations, the combined method of the Laplace Transform Method and the Adomian Decomposition Method is used. As a result, series solutions of the equations are constructed. In order to explore the rapid decay of the equations, the pade approximation is used. The results present validity and great potential of the method as a powerful al...

in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerica...

The aim of this paper is to present the application of the analytical series technique to study properties of the nonlinear chaotic dynamical systems. More specifically, Laplace–Adomian decomposition method is applied to Rössler system and the so-called generalized Lorenz system. Some advantages and possible applications of this approach are discussed. Results are illustrated by numerical compu...

In this paper, a numerical Laplace transform algorithm which is based on the decomposition method is introduced for the approximate solution of a class of nonlinear differential equations. The technique is described and illustrated with some numerical examples. The results assert that this scheme is rapidly convergent and quite accurate by which it approximates the solution using only few terms...

In this paper, we propose an effective iterative preconditioning method to solve elliptic problems with jumps in coefficients. The algorithm is based on the additive Schwarz method (ASM). First, we consider a domain decomposition method without ‘cross points’ on interfaces between subdomains and the second is the ‘cross points’ case. In both cases the main computational cost is an implementatio...

We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The ...