Results 61 to 70 of about 1,280 (181)

The decomposition method: Adomian decomposition method

, 2021
Firstly, in this study, Adomian Decomposition Method is explained on problems which are in different types are related ordinary differential, partial differential and integral equations. The main purpose of this study is to examine the effect of thermal flux applied to a thick-walled cylinder which is made by composite materials.
openaire   +1 more source

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
Nonlinear dispersion phenomena in liquid media often lead to the formation of localized structures such as compact wave packets and dispersion drops. The present investigation demonstrates that the proposed analytical framework yields accurate approximate solutions, successfully captures compacton‐like structures, and clearly reveals the critical ...
Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed, Rajesh Kumar   +3 more
wiley   +1 more source

Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Abstract and Applied Analysis, 2013
Two tecHniques were implemented, the Adomian decomposition method (ADM) and multivariate Padé approximation (MPA), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense.
Veyis Turut, Nuran Güzel
doaj   +1 more source

The Adomian Decomposition Method for Eigenvalue Problems

Journal of Applied & Computational Mathematics, 2016
The Adomian decomposition method (ADM) is a powerful method which considers the approximate solution of a non-linear equation as an infinite series which usually converges to the exact solution. In this paper, this method is proposed to solve some eigenvalue problems.
Nhawu G, Mafuta P
openaire   +1 more source

Improved Analytical Technique Based on Laplace Transform and Homotopy Perturbation Method for Solving Fractional Bratu‐Type Equations

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This study presents a modified Laplace transform homotopy perturbation method (MLT‐HPM) for obtaining approximate solutions for fractional‐order Bratu‐type ordinary differential equations involving Caputo fractional derivatives. The proposed modification introduces a specific rule for selecting the initial solution, replacing the conventional random ...
Ibrahim Hailat, Patricia J. Y. Wong
wiley   +1 more source

The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM) [PDF]

Computational Ecology and Software, 2016
The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems.
Hafiz Abdul Wahab, Saira Bhatti, Mohammad Naeem   +2 more
doaj  

Numerical analysis of Lane Emden–Fowler equations

Journal of Taibah University for Science, 2018
This paper is devoted to the numerical solutions of Lane Emden–Fowler partial differential equations. For the numerical analysis, we apply Laplace transform coupled with the Adomian decomposition method known as the Laplace Adomian decomposition method ...
Atta Ullah, Kamal Shah
doaj   +1 more source

Application of the Adomian decomposition method for the Fokker–Planck equation

Mathematical and Computer Modelling, 2007
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Mehdi Tatari, Mehdi Dehghan 0002, Mohsen Razzaghi   +2 more
openaire   +2 more sources

Existence and Uniqueness of Nonlinear Volterra Integral Equations With Variable Fractional Order in Fréchet Spaces via a Frigon−Granas Fixed Point Approach

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper investigates the existence and uniqueness of solutions to nonlinear Volterra integral equations of variable fractional order in Fréchet spaces. The variable‐order fractional derivative is considered in the Riemann–Liouville sense, which extends classical approaches and is central to the paper’s novelty.
Mohamed Telli, Benoumran Telli, Mohammed Said Souid, K. Sudarmozhi, Joshua Kiddy K. Asamoah, Khalil Ezzinbi   +5 more
wiley   +1 more source

Numerical and Analytical Solutions for a Nonlinear System

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper investigates two nonlinear reaction–diffusion systems: (i) a spatially extended competitive species model and (ii) the FitzHugh–Nagumo system, which serves as a canonical model of excitable media. For the first system, we derive exact closed‐form solutions using the exponential function method; these solutions exhibit spatially periodic ...
Badran Jasim Salim, Dalya Mahmood Merie, Deepali   +2 more
wiley   +1 more source