Solving a Class of High Order Non-linear Partial Differential Systems Using Adomian Decomposition Method

2018 ◽  
Vol 14 (2) ◽  
pp. 76-93
Author(s):  
Ahmed Farooq Qasim ◽  
◽  
Mohammed Azeez Hilal
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
High Order ◽  
Partial Differential ◽  
Differential Systems ◽  
Adomian Decomposition ◽  
Non Linear

scholarly journals Approximate analytical solutions of non-linear local fractional heat equations

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 837-841 ◽  
Author(s):  
Shuxian Deng
Keyword(s):  
Analytical Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Heat Equations ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Fractional Heat Equation ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Non Linear

Consider the non-linear local fractional heat equation. The fractional complex transform method and the Adomian decomposition method are used to solve the equation. The approximate analytical solutions are obtained.

scholarly journals Exact Solution of Space-Time Fractional Partial Differential Equations by Adomian Decomposition Method

2021 ◽  
pp. 75-87
Author(s):  
Vidya N. Bhadgaonkar ◽  
Bhausaheb R. Sontakke
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Adomian Decomposition Method ◽  
Physical Models ◽  
Partial Differential ◽  
Conduction Model ◽  
Adomian Decomposition ◽  
Present Technique

The intention behind this paper is to achieve exact solution of one dimensional nonlinear fractional partial differential equation(NFPDE) by using Adomian decomposition method(ADM) with suitable initial value. These equations arise in gas dynamic model and heat conduction model. The results show that ADM is powerful, straightforward and relevant to solve NFPDE. To represent usefulness of present technique, solutions of some differential equations in physical models and their graphical representation are done by MATLAB software.

scholarly journals New optical explicit plethora of the resonant Schrodinger’s equation via two recent computational schemes

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 247-255
Author(s):  
Mostafa Khater ◽  
Abdel-Haleem Abdel-Aty ◽  
Ghada Alnemer ◽  
Mohammed Zakarya ◽  
Dianchen Lu
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Research Paper ◽  
Linear Optics ◽  
Computational Schemes ◽  
Non Linear Optics ◽  
Wave Solutions ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Schrödinger's Equation

This research paper investigates the computational solutions of the resonant Schr?dinger?s equation. The modified Khater method and Adomian decomposition method are applyied for construct new analytical traveling and semi-analytical wave solutions. This model describes the pulse phenomena and studied in non-linear optics. For further illustration of our obtained solutions, some distinct types of sketches are given.

Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

2021 ◽  
Vol 20 ◽  
pp. 712-716
Author(s):  
Zainab Mohammed Alwan
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Integral Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Adomian Decomposition

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method

2014 ◽  
Vol 6 (01) ◽  
pp. 107-119 ◽  
Author(s):  
D. B. Dhaigude ◽  
Gunvant A. Birajdar
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Diffusion Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Discrete Schrödinger Equation ◽  
Adomian Decomposition

AbstractIn this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method. Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation, nonlinear fractional discrete Schrodinger equation, fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger’s equation. The obtained solution is verified by comparison with exact solution whenα= 1.

Sign in / Sign up

Export Citation Format

Share Document