scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Application of Natural Transform Method to Fractional Pantograph Delay Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
M. Valizadeh ◽  
Y. Mahmoudi ◽  
F. Dastmalchi Saei
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
New Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Delay Differential

In this paper, a new method based on combination of the natural transform method (NTM), Adomian decomposition method (ADM), and coefficient perturbation method (CPM) which is called “perturbed decomposition natural transform method” (PDNTM) is implemented for solving fractional pantograph delay differential equations with nonconstant coefficients. The fractional derivative is regarded in Caputo sense. Numerical evaluations are included to demonstrate the validity and applicability of this technique.

scholarly journals Variational Approximate Solutions of Fractional Delay Differential Equations with Integral Transform

2021 ◽  
pp. 3679-3689
Author(s):  
Eman Mohmmed Namah
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Integral Transform ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Adomian Decomposition ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

     The idea of the paper is to consolidate Mahgoub transform and variational iteration method (MTVIM) to solve fractional delay differential equations (FDDEs). The fractional derivative was in Caputo sense. The convergences of approximate solutions to exact solution were quick. The MTVIM is characterized by ease of application in various problems and is capable of simplifying the size of computational operations.  Several non-linear (FDDEs) were analytically solved as illustrative examples and the results were compared numerically. The results for accentuating the efficiency, performance, and activity of suggested method were shown by comparisons with Adomian Decomposition Method (ADM), Laplace Adomian Decomposition Method (LADM), Modified Adomian Decomposition Method (MADM) and Homotopy Analysis Method (HAM).

Solving Nonlinear Volterra | Fredholm Integro-differential Equations Using the Modified Adomian Decomposition Method

2009 ◽  
Vol 9 (4) ◽  
pp. 321-331 ◽  
Author(s):  
M. A. Fariborzi Araghi ◽  
Sh. Sadigh Behzadi
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Error Bound ◽  
Decomposition Method ◽  
Numerical Scheme ◽  
Adomian Decomposition Method ◽  
Integro Differential Equation ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

AbstractIn this paper, a nonlinear Volterra | Fredholm integro-differential equation is solved by using the modified Adomian decomposition method (MADM). The approximate solution of this equation is calculated in the form of a series in which its components are computed easily. The accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results. The existence, uniqueness and convergence and an error bound of the proposed method are proved. Some examples are presented to illustrate the efficiency and the performance of the modified decomposition method.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

scholarly journals Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

2019 ◽  
Vol 24 (1) ◽  
pp. 7 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Asmaa Al-Enazi ◽  
Bassam Z. Albalawi ◽  
Mona D. Aljoufi
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Surface Brightness ◽  
Milky Way ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Canonical Forms ◽  
Exponential Functions ◽  
Adomian Decomposition ◽  
Delay Differential

The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature.

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