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

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.

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Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method

Open Physics ◽

10.1515/phys-2020-0104 ◽

2020 ◽

Vol 18 (1) ◽

pp. 182-188

Author(s):

O. González-Gaxiola ◽

Anjan Biswas ◽

Abdullah Kamis Alzahrani

Keyword(s):

Numerical Simulations ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Optical Solitons ◽

Decomposition Scheme ◽

Error Analyses ◽

Adomian Decomposition ◽

Log Law

AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

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A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

Advances in Difference Equations ◽

10.1186/s13662-020-02981-7 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Hassan Eltayeb ◽

Imed Bachar ◽

Yahya T. Abdalla

Keyword(s):

Numerical Simulation ◽

Approximate Solution ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Approximate Solutions ◽

Navier Stokes ◽

Two Dimensional ◽

Navier Stokes Equation ◽

Adomian Decomposition ◽

Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

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

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v4i4.4965 ◽

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.

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The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method

Open Physics ◽

10.1515/phys-2018-0097 ◽

2018 ◽

Vol 16 (1) ◽

pp. 780-785 ◽

Cited By ~ 10

Author(s):

Sunday O. Edeki ◽

Tanki Motsepa ◽

Chaudry Masood Khalique ◽

Grace O. Akinlabi

Keyword(s):

Analytical Solution ◽

Option Pricing ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Asian Option ◽

Pricing Model ◽

Adomian Decomposition ◽

Option Pricing Model ◽

Option Model ◽

High Level

Abstract The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

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Convergence of the New Iterative Method

International Journal of Differential Equations ◽

10.1155/2011/989065 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10 ◽

Cited By ~ 22

Author(s):

Sachin Bhalekar ◽

Varsha Daftardar-Gejji

Keyword(s):

Iterative Method ◽

Functional Equations ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Efficient Technique ◽

Nonlinear Functional ◽

Adomian Decomposition ◽

New Iterative Method ◽

Sufficiency Conditions

A new iterative method introduced by Daftardar-Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence of DJM and Adomian decomposition method is established.

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A Comparison between Adomian Decomposition and Tau Methods

Abstract and Applied Analysis ◽

10.1155/2013/621019 ◽

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.

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Numerical Solution of Time-Fractional Klein–Gordon Equation by Using the Decomposition Methods

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4032767 ◽

2016 ◽

Vol 11 (4) ◽

Cited By ~ 11

Author(s):

Hossein Jafari

Keyword(s):

Iterative Method ◽

Numerical Solution ◽

Decomposition Method ◽

Gordon Equation ◽

Adomian Decomposition Method ◽

Type Equation ◽

Decomposition Methods ◽

Adomian Decomposition ◽

Klein Gordon ◽

Klein Gordon Equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

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Solving Fractional-Order Logistic Equation Using a New Iterative Method

International Journal of Differential Equations ◽

10.1155/2012/975829 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12 ◽

Cited By ~ 11

Author(s):

Sachin Bhalekar ◽

Varsha Daftardar-Gejji

Keyword(s):

Iterative Method ◽

Perturbation Method ◽

Decomposition Method ◽

Homotopy Perturbation Method ◽

Adomian Decomposition Method ◽

Logistic Equation ◽

Series Solutions ◽

Homotopy Perturbation ◽

Adomian Decomposition ◽

New Iterative Method

A fractional version of logistic equation is solved using new iterative method proposed by Daftardar-Gejji and Jafari (2006). Convergence of the series solutions obtained is discussed. The solutions obtained are compared with Adomian decomposition method and homotopy perturbation method.

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