scholarly journals A comparison of Adomian decomposition method and RK4 algorithm on Volterra integro differential equations of 2nd kind

2015 ◽  
Vol 4 (4) ◽  
pp. 481
Author(s):  
Kekana M.C ◽  
Shatalov M.Y ◽  
Moshokoa S.P
Keyword(s):  
Differential Equations ◽  
Infinite Series ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Adomian Decomposition

In this paper, Volterra Integro differential equations are solved using the Adomian decomposition method. The solutions are obtained in form of infinite series and compared to Runge-Kutta4 algorithm. The technique is described and illustrated with examples; numerical results are also presented graphically. The software used in this study is mathematica10.

scholarly journals A Comparison between Adomian Decomposition and Tau Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Necdet Bildik ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Tau Method ◽  
Adomian Decomposition

We present a comparison between Adomian decomposition method (ADM) and Tau method (TM) for the integro-differential equations with the initial or the boundary conditions. The problem is solved quickly, easily, and elegantly by ADM. The numerical results on the examples are shown to validate the proposed ADM as an effective numerical method to solve the integro-differential equations. The numerical results show that ADM method is very effective and convenient for solving differential equations than Tao method.

scholarly journals Adomian Decomposition Method with Orthogonal Polynomials: Laguerre Polynomials and the Second Kind of Chebyshev Polynomials

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1796
Author(s):  
Yingying Xie ◽  
Lingfei Li ◽  
Mancang Wang
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Laguerre Polynomials ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

In this paper, a new efficient and practical modification of the Adomian decomposition method is proposed with Laguerre polynomials and the second kind of Chebyshev polynomials which has not been introduced in other articles to the best of our knowledge. This approach can be utilized to approximately solve linear and nonlinear differential equations. The proposed formulations are examined by a representative example and the numerical results confirm their efficiency and accuracy.

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 Numerical Simulation of Cubic-Quartic Optical Solitons with Perturbed Fokas–Lenells Equation Using Improved Adomian Decomposition Algorithm

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 138
Author(s):  
Alyaa A. Al-Qarni ◽  
Huda O. Bakodah ◽  
Aisha A. Alshaery ◽  
Anjan Biswas ◽  
Yakup Yıldırım ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Iterative Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Numerical Results ◽  
Decomposition Algorithm ◽  
Adomian Decomposition ◽  
High Level ◽  
Do So

The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known results in the literature. As proven, the proposed scheme is efficient and possess a high level of accuracy.

scholarly journals The Modified Sadik Decomposition Method to Solve a System of Nonlinear Fractional Volterra Integro-Differential Equations of Convolution type

2021 ◽  
Vol 20 ◽  
pp. 335-343
Author(s):  
Prapart Pue-On
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Explicit Form ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Solution ◽  
Convolution Type ◽  
Adomian Decomposition

In this work, an incorporated form of Sadik transform and Adomian decomposition method which is called the Sadik decomposition method is presented. The method is applied to solve a system of nonlinear fractional Volterra integro-differential equations in the convolution form. To avoid collecting the noise terms that lead the method to fail for seeking the solution, the proposed method is modified by selecting a suitable initial solution. The obtained results are expressed in the explicit form of a power series with easily computable terms. In addition, illustrative examples are shown to demonstrate the effectiveness of the method.

scholarly journals Application of Adomian decomposition method to solve hybrid fuzzy differential equations

2015 ◽  
Vol 9 (1) ◽  
pp. 95-103 ◽  
Author(s):  
Mahmoud Paripour ◽  
Elahe Hajilou ◽  
Afshin Hajilou ◽  
Homa Heidari
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition
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