Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved.  Uniqueness and converg...

In this paper, we show that with a few modifcations and techniques the Adomian Decomposition Method (ADM) for solving a class of hyperbolic equations with nonlocal conditions can be applied to obtain the exact solutions to this type of problems. The clue of this one consists in transforming the boundary value nonlocal problem into a classical problem whose solution is obtained.

*Correspondence: [email protected] 1Department of Mathematical Sciences, University of Karachi, Karachi, 75270, Pakistan Full list of author information is available at the end of the article Abstract The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has ...

In this article the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered. Mathematical modeling of the problem leads to a system of non-linear ordinary differential equations. Adomian decomposition method is employed to solve this system of nonlinear ordinary differential equations, the problem of conve...

By considering the Adomian decomposition scheme, we solve a generalized Boussinesq equation. The method does not need linearization or weak nonlinearly assumptions. By using this scheme, the solutions are calculated in the form of a convergent power series with easily computable components. The decomposition series analytic solution of the problem is quickly obtained by observing the existence ...

An abstract result is proved for the convergence of Adomian decomposition method for partial differential equations that model evolutionary systems. Moreover, we prove that this decomposition scheme applied to a system of wave equations coupled in parallel with homogeneous Dirichlet boundary conditions, is convergent in a suitable Hilbert space. Furthermore, this technique is utilized to find c...

Laplace decomposition method is based on Laplace transform method and Adomian decomposition method. In this paper we show that the method is applicable to certain successive interval valued linear as well as nonlinear differential-difference equations of order (1, 2), that means the differential is of order one and the difference is of order two. It is also shown that the method gives exact sol...