Since 2001, Laplace decomposition algorithm (LDA) has been one of the reliable mathematical methods for obtaining exact or numerical approximation solutions for a wide range of nonlinear problems. The Laplace decomposition algorithm was developed by Khuri in [2] to solve a class of nonlinear differential equations. The basic idea in Laplace decomposition algorithm, which is a combined form of t...

This paper is concerned with a thorough investigation in achieving exact analytical solution for the Van der Pol (VDP) nonlinear oscillators models via Adomian decomposition method (ADM). The are time dependent second order ordinary differential equations. ADM has already been applied, existing literatures, to obtain approximate results. But, we adapt by adjusting source term; procedure that ba...

This article uses two separate approaches to find reliable and estimated solutions for the weakly nonlinear shallow-water wave model, which explains these waves are spreading in a thin dispersive medium. Exact achieved by utilizing an expanded tanh expansion Adomian decomposition (ADM.). We also evaluate demonstrate how closely they are; all convincing persuasive partial differential equations.

In this paper, it is revealed that Adomian decomposition method corresponds to Taylor series method when applied to the solution of nonlinear initial value problems, in the following sense: the Adomian ́s polynomials can be obtain trough Taylor coefficients.

Decomposition method was first introduced by Adomian since the beginning of the 1980’s for solving wide range of problems whose mathematical models yield equation or system of equation involving algebraic, differential, integral and integro-diffrential [1, 2, 3]. This iterative method has been proven to be rather successful in dealing with linear problems as well as nonlinear. Adomian gives the...

In this manuscript, we study a nonlinear fractional-order predator-prey system while considering uncertainty in initial values. We derive the feasibility region and boundness of solution. The suggested model’s equilibrium points basic reproduction number are calculated. stability is presented. use metric fixed point theory to existence uniqueness results concerning solution model. notion UH-sta...

In this paper, the solution methodology of higher-order linear fractional partial deferential equations (FPDEs) as mentioned in eqs (1) and (2) below Caputo definition relies on a new analytical method which is called Laplace-residual power series (L-RPSM). The main idea our proposed technique to convert original FPDE Laplace space, then apply residual (RPSM) by using concept limit obtain solut...

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

In this paper, theAdomiandecompositionmethod and Padé approximants are integrated to study thedeflection andpull-in instability of nanocantilever electromechanical switches. In a distributed parameter model, intermolecular forces, including Casimir forces, are taken into account considering their range of application. A closed form power series solution based on Adomian polynomials is obtained....

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 proposed methods ...