Exact solution of certain time fractional nonlinear partial differential equations

2016 ◽  
Vol 85 (1) ◽  
pp. 659-673 ◽  
Author(s):  
R. Sahadevan ◽  
P. Prakash
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential

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.

scholarly journals Recent Modification of Decomposition Method for Solving Nonlinear Partial Differential Equations

2020 ◽  
Vol 18 ◽  
pp. 154-161
Author(s):  
Zainab Hadi Kareem ◽  
Luma Naji Mohammed Tawfiq
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Problems ◽  
Convergent Series ◽  
Partial Differential ◽  
Strongly Nonlinear ◽  
Recent Modification

In this paper, efficient modification of Adomain decomposition method is proposed to solve nonlinear partial differential equations. Yields solution in rapid convergent series from easily computable terms to get exact solution, and yields in few iterations we get exact solution. Moreover, this modification does not require any linearization, discretization, or perturbations and therefore reduces the computations. Two illustration examples are introduced and illustrate the procedure of modification is simple yet highly accurate and rapidly converge to exact solution compares with the ADM or other modifications. The methodology presented here is useful for strongly nonlinear problems.

scholarly journals Approximate Solution of Fractional Nonlinear Partial Differential Equations by the Legendre Multiwavelet Galerkin Method

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
M. A. Mohamed ◽  
M. Sh. Torky
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Nonlinear Partial Differential Equations ◽  
Algebraic Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
The Galerkin Method

The Legendre multiwavelet Galerkin method is adopted to give the approximate solution for the nonlinear fractional partial differential equations (NFPDEs). The Legendre multiwavelet properties are presented. The main characteristic of this approach is using these properties together with the Galerkin method to reduce the NFPDEs to the solution of nonlinear system of algebraic equations. We presented the numerical results and a comparison with the exact solution in the cases when we have an exact solution to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Sign in / Sign up

Export Citation Format

Share Document