scholarly journals Behaviour Analysis of the Padé Sumudu Adomian Decomposition Method Solution

2021 ◽  
pp. 39-45
Author(s):  
Richard Metonou ◽  
Zhao Weidong
Keyword(s):  
Decomposition Method ◽  
Schrodinger Equation ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Pade Approximation ◽  
Approximation Solution ◽  
Behaviour Analysis ◽  
The Past ◽  
Adomian Decomposition

Researchers in the past investigate the Sumudu Adomian Decomposition Method (SADM), the Laplace Adomian Decomposition Method (LADM), the Padé Sumudu Adomian Decomposition Methods (PSADM). In this paper we analyse the behaviour of the function P[L/M][.] called double Padé approximation using in the Padé Sumudu Adomian Decomposition Method (PSADM), and provide some criteriums for chosing L and M to obtain the best Padé approximation solution in the case of nonlinear Schrödinger equation and nonlinear KdV Burger's equation.

scholarly journals Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Metomou Richard ◽  
Weidong Zhao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Decomposition Method ◽  
Schrodinger Equation ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Pade Approximation ◽  
Nonlinear Schrödinger ◽  
Adomian Decomposition

The main purpose of this paper is to solve the nonlinear Schrödinger equation using some suitable analytical and numerical methods such as Sumudu transform, Adomian Decomposition Method (ADM), and Padé approximation technique. In many literatures, we can see the Sumudu Adomian decomposition method (SADM) and the Laplace Adomian decomposition method (LADM); the SADM and LADM provide similar results. The SADM and LADM methods have been applied to solve nonlinear PDE, but the solution has small convergence radius for some PDE. We perform the SADM solution by using the function P L / M · called double Padé approximation. We will provide the graphical numerical simulations in 3D surface solutions of each application and the absolute error to illustrate the efficiency of the method. In our methods, the nonlinear terms are computed using Adomian polynomials, and the Padé approximation will be used to control the convergence of the series solutions. The suggested technique is successfully applied to nonlinear Schrödinger equations and proved to be highly accurate compared to the Sumudu Adomian decomposition method.

scholarly journals Approximate Solution of Riccati Differential Equation via Modified Greens Decomposition Method

2020 ◽  
Vol 70 (4) ◽  
pp. 419-424
Author(s):  
Amit Ujlayan ◽  
Mohit Arya
Keyword(s):  
Numerical Solution ◽  
Decomposition Method ◽  
Padé Approximation ◽  
Medical Science ◽  
Adomian Decomposition Method ◽  
Specific Class ◽  
Pade Approximation ◽  
Riccati Differential Equation ◽  
Adomian Polynomials ◽  
Adomian Decomposition

Riccati differential equations (RDEs) plays important role in the various fields of defence, physics, engineering, medical science, and mathematics. A new approach to find the numerical solution of a class of RDEs with quadratic nonlinearity is presented in this paper. In the process of solving the pre-mentioned class of RDEs, we used an ordered combination of Green’s function, Adomian’s polynomials, and Pade` approximation. This technique is named as green decomposition method with Pade` approximation (GDMP). Since, the most contemporary definition of Adomian polynomials has been used in GDMP. Therefore, a specific class of Adomian polynomials is used to advance GDMP to modified green decomposition method with Pade` approximation (MGDMP). Further, MGDMP is applied to solve some special RDEs, belonging to the considered class of RDEs, absolute error of the obtained solution is compared with Adomian decomposition method (ADM) and Laplace decomposition method with Pade` approximation (LADM-Pade`). As well, the impedance of the method emphasised with the comparative error tables of the exact solution and the associated solutions with respect to ADM, LADM-Pade`, and MGDMP. The observation from this comparative study exhibits that MGDMP provides an improved numerical solution in the given interval. In spite of this, generally, some of the particular RDEs (with variable coefficients) cannot be easily solved by some of the existing methods, such as LADM-Pade` or Homotopy perturbation methods. However, under some limitations, MGDMP can be successfully applied to solve such type of RDEs.

scholarly journals Adomian Decomposition Method Combined with Padé Approximation and Laplace Transform for Solving a Model of HIV Infection of CD4+T Cells

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fang Chen ◽  
Qing-Quan Liu
Keyword(s):  
T Cells ◽  
Approximate Solution ◽  
Hiv Infection ◽  
Laplace Transform ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Pade Approximation ◽  
Adomian Decomposition

The classical Adomian decomposition method (ADM) is implemented to solve a model of HIV infection of CD4+T cells. The results indicate that the approximate solution by using the ADM is the same as that by using the Laplace ADM, but it can be obtained in a more efficient way. We also use Padé approximation and Laplace transform as a posttreatment technique to obtain the result of the ADM. The advantage of the posttreatment is illustrated by numerical experiments.

scholarly journals On the Study of Oscillating Viscous Flows by Using the Adomian-Padé Approximation

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Chi-Min Liu
Keyword(s):  
Fourier Analysis ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Viscous Flows ◽  
Pulsating Flow ◽  
Pade Approximation ◽  
Oscillating Flows ◽  
Approximation Solution ◽  
Adomian Decomposition ◽  
Stokes Second Problem

The Adomian-Padé technique is applied to examine two oscillating viscous flows, the Stokes’ second problem and the pressure-driven pulsating flow. Main purposes for studying oscillating flows are not only to verify the accuracy of the approximation solution, but also to provide a basis for analyzing more problems by the present method with the help of Fourier analysis. Results show that the Adomian-Padé approximation presents a very excellent behavior in comparison with the exact solution of Stokes’ second problem. For the pulsating flow, only the Adomian decomposition method is required to perform the calculation as the fluid domain is finite where the Padé approximant may not provide a better solution. Based on present results, more problems can be mathematically solved by using the Adomian-Padé technique, the Fourier analysis, and powerful computers.

APPROXIMATE SOLUTION FOR TIME-DELAYED CONVECTIVE FISHER EQUATION BY ADM-PADÉ TECHNIQUE

2010 ◽  
Vol 03 (02) ◽  
pp. 221-233 ◽  
Author(s):  
A. Alharbi ◽  
E. S. Fahmy
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Fisher Equation ◽  
Pade Approximation ◽  
Adomian Decomposition

We present an approximate solution to the time-delayed convective Fisher equation using ADM-Padé technique which is a combination of Adomian decomposition method and Padé approximation. This technique gives the approximate solution with faster convergence and higher accuracy than using ADM alone.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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

2016 ◽  
Vol 11 (4) ◽  
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.

scholarly journals Solution of the Black-Scholes Equation: LDM and SDM

2021 ◽  
Vol 23 (07) ◽  
pp. 1111-1115
Author(s):  
R. K. Pavan Kumar. Pannala ◽  
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Financial Mathematics ◽  
Discretization Method ◽  
Discretization Methods ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Laplace Decomposition Method

The main aim of this paper is to discuss a new way of a non-discretization method for the solution of the Black-Scholes equation. Black-Scholes is a mathematical model based on a partial differential equation. The solution of the model is of utmost importance in financial mathematics to estimate option pricing. Several analytical, numerical, and non-discretization methods are existing in the literature to solve the model. Two decomposition methods namely the Laplace decomposition method (LDM) and Sumudu decomposition method (SDM) are adopted for the present study. The results of the present techniques have closed an agreement with an approximate solution which has been obtained with the help of the Adomian Decomposition Method (ADM).

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