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, we apply the Fourier transform method with Adomian decomposition to solve Riccati equations . Proposed is based on and adomian methods. The solutions obtained using FADMs are compared numerical Rung Kutta2 Euler method. Also, error graphs of presented.

Large classes of linear and nonlinear differential equations, both ordinary as well as partial, can be solved by the Adomian decomposition method [3, 4, 6]. This method is much more simpler in computation and quicker in convergence than any other method available in the open literature. The application of the fractional differential equation in physical problems is available in the book of Brac...

To find the explicit solutions of nonlinear differential equations, many powerful methods have been used (Abbasbandy, 2006; He, 1998; Wazwaz, 1997; Ghasemi et al., 2007; Adomian and Adomian, 1984). The homotopy analysis method (HAM) (Liao, 2003, 2004; Liao and Tan, 2007; Yamashita et al., 2007) is a general analytic approach to get series solutions of various types of nonlinear equations. The H...

In this work we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Adomian decomposition method for solving the Fokker–Planck equation and some similar equations. ...

*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 paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.