Solution of the Nonlinear Kompaneets Equation Through the Laplace-Adomian Decomposition Method

González-Gaxiola, O.; Chávez, Juan Ruíz de; Bernal-Jáquez, R.

doi:10.1007/s40819-016-0144-0

Cited by 4 publications

(4 citation statements)

References 43 publications

(90 reference statements)

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“…The initial (or the border conditions) and the terms that contain the independent variables will be considered as the initial approximation. In this way and by means of a recurrence relations, it is possible to find the terms of the series that give the approximate solution of the differential equation (see [14]). Given a partial (or ordinary) differential equation…”

Section: 2mentioning

confidence: 99%

“…But some evolution problems do not admit the traveling wave solutions, due to that, we propose a semianalytical method called Laplace Adomian Decomposition Method (LADM), it is a combination of the Adomian Decomposition Method (ADM) and Laplace transforms. This method was successfully used for solving different problems in [5,8,14,18,20,23,37,40]. The ADM was introduced by Adomian [1][2][3][4] and has been applied to a wide class of problems in physics, biology and chemical reactions.…”

Section: Introductionmentioning

confidence: 99%

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Exact Solutions of Kupershmidt Equation, Approximate Solutions for Time-Fractional Kupershmidt Equation: A Comparison Study

Djilali

Hakem

Benali

2020

ijaa

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In this article, a technique namely Tanh method is applied to obtain some traveling wave solutions for Kupershmidt equation, and by using LADM we obtain an approximate solution to timefractional Kupershmidt equation. A comparison between the traveling wave solution (exact solution) and the approximate one of equation under study, indicate that Laplace Adomian Decomposition Method (LADM) is highly accurate and can be considered a very useful and valuable method.

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Section: 2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Kupershmidt Equation, Approximate Solutions for Time-Fractional Kupershmidt Equation: A Comparison Study

Djilali

Hakem

Benali

2020

ijaa

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“…The SDIQR mathematical modelling for Covid-19 of Odisha based on Laplace Adomian decomposition method is employed by Sahu and Jena [30] and Jena and Sahu [58] solved the fractional nonlinear evolution equation by using Shehu transform. Laplace decomposition method is also employed to solve nonlinear Kompaneets equation by González-Gaxiola et al [11] and nonlinear Klein-Gordon equation by Emad et al [13]. Manzoor et al [12] used Adomian decomposition method for space time fractional Telegraph equation.…”

Section: Introductionmentioning

confidence: 99%

A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

Jena,

Sahu

2023

Phys. Scr.

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In this paper we investigate approximate analytical solution so called voltage in one and two space variables for linear and nonlinear telegraph equations by a reliable method namely Modified Laplace Decomposition Method (MLDM) using MATLAB and MATHEMATICA software tools. The MLDM is a mixture of Laplace transform with modified Adomian decomposition method based on Newton Raphson method. The nonlinearity of the problem is tackled by Adomian decomposition and approximate analytical solution to the partial differential equation handled by using the Laplace and inverse Laplace transform technique without differentiation in time domain. We use Newton Raphson method in the domain of Adomian polynomial to modify it. Theoretical concepts for the approximate analytical solution of present scheme are well behaved through stability and convergence analysis. Five numerical examples are carried out in order to check the effectiveness and applicability of the proposed scheme. The telegraph equation with one space variable is solved numerically whereas the approximate analytical solution obtained for two space variables. Employing MLDM, it is possible to obtain the approximate analytical solution (i.e., voltage) of a telegraph equation and found to be in good agreement with exact solutions and also compared with earlier studies for one space variable.

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“…This approach can be used for the extremely precise analytical calculation of the orbit of the planet Mercury, for the study of its perihelion precession, as well as for the computation of the light deflection by the Sun. The solutions of the Kompaneets equation, a nonlinear partial differential equation that plays an important role in astrophysics, describing the spectra of photons in interaction with a rarefied electron gas, were obtained, by using the Laplace-Adomian Decomposition Method, in González-Gaxiola et al (2017).…”

Section: Introductionmentioning

confidence: 99%

A Brief Introduction to the Adomian Decomposition Method, with Applications in Astronomy and Astrophysics

Mak,

Leung,

Harko

2021

Preprint

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The Adomian Decomposition Method (ADM) is a very effective approach for solving broad classes of nonlinear partial and ordinary differential equations, with important applications in different fields of applied mathematics, engineering, physics and biology. It is the goal of the present paper to provide a clear and pedagogical introduction to the Adomian Decomposition Method and to some of its applications. In particular, we focus our attention to a number of standard first-order ordinary differential equations (the linear, Bernoulli, Riccati, and Abel) with arbitrary coefficients, and present in detail the Adomian method for obtaining their solutions. In each case we compare the Adomian solution with the exact solution of some particular differential equations, and we show their complete equivalence. The second order and the fifth order ordinary differential equations are also considered. An important extension of the standard ADM, the Laplace-Adomian Decomposition Method is also introduced through the investigation of the solutions of a specific second order nonlinear differential equation. We also present the applications of the method to the Fisher-Kolmogorov second order partial nonlinear differential equation, which plays an important role in the description of many physical processes, as well as three important applications in astronomy and astrophysics, related to the determination of the solutions of the Kepler equation, of the Lane-Emden equation, and of the general relativistic equation describing the motion of massive particles in the spherically symmetric and static Schwarzschild geometry.

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Solution of the Nonlinear Kompaneets Equation Through the Laplace-Adomian Decomposition Method

Cited by 4 publications

References 43 publications

Exact Solutions of Kupershmidt Equation, Approximate Solutions for Time-Fractional Kupershmidt Equation: A Comparison Study

Exact Solutions of Kupershmidt Equation, Approximate Solutions for Time-Fractional Kupershmidt Equation: A Comparison Study

A reliable method for voltage of telegraph equation in one and two space variables in electrical transmission: approximate and analytical approach

A Brief Introduction to the Adomian Decomposition Method, with Applications in Astronomy and Astrophysics

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