Solution of the System of Ordinary Differential Equations by Combined Laplace Transform–Adomian Decomposition Method

Doğan, Nurettin

doi:10.3390/mca17030203

Cited by 16 publications

(13 citation statements)

References 7 publications

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“…Moreover, one can find in Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24] other interesting applications of the LT.…”

Section: Introductionmentioning

confidence: 99%

A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution

Mahrous

2021

ijaa

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This paper discusses a possible generalization of the transport model describing the chlorine concentration decay in pipes. The proposed generalized model is governed by a second-order fractional partial differential equation. The exact solution of the generalized model is obtained via the Laplace transform method and the method of residues. The exact solution reduces to the corresponding published one as the fractional order α tends to one. Analytical expression for the dimensionless cup-mixing average concentration is deduced. Influences of various parameters on the behavior of the dimensionless cup-mixing average concentration are discussed. It is shown that the physical interpretation of the dimensionless cup-mixing average concentration in view of the fractional calculus is completely different than its interpretation in the classical calculus.

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“…Moreover, one can find in Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24] other interesting applications of the LT.…”

Section: Introductionmentioning

confidence: 99%

A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution

Mahrous

2021

ijaa

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“…To solve this problem, He's Variational Iteration Method [10], Homotopy Perturbation Method [11] and Variational Iteration Method [3] have been used. The aim of this paper is to extend the use of LADM [1,[4][5][6][7][8][9]12] in order to obtain estimated solution of the pollution model.…”

Section: Introductionmentioning

confidence: 99%

Series Solution of Modelling the Pollution

Doğan

2021

Turkish Journal of Mathematics and Computer Science

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In this article, an approximate analytical series solution of Modeling the pollution of a lake system is given. Laplace-Adomian decomposition method (LADM) was used for the serial solution. LADM with different input values has been used for the solution. The solutions obtained by LADM were compared with the results obtained by Fourth Order Runge Method. In addition, the results are compared with residual errors. These comparisons show that LADM is a powerful method for obtaining approximate solutions to the problem of modeling the pollution of a lake system.

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“…However, it is still very difficult to obtain closed-form solutions for most models of real-life problems. A broad class of analytical and numerical methods were used to handle such problems such as variational iteration method [1][2][3][4][5][6], Adomian decomposition method [7][8][9][10], homotopy perturbation method [11][12][13][14][15][16][17], new iterative method [18][19][20][21][22][23][24][25] and integral iterative method [26,27]. It is worth mentioning that the new iterative, homotopy perturbation and integral iterative methods are applied without any discretization, restrictive assumption or transformation and are free from round off errors.…”

Section: Introductionmentioning

confidence: 99%

Analytical techniques for solving the equation governing the unsteady flow of a polytropic gas with time-fractional derivative

Eladdad¹,

Tarif²

2020

Filomat

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In this work, some analytical techniques viz. homotopy perturbation method, new iterative method and integral iterative method are used to solve nonlinear fractional differential equations such as the equation governing the unsteady flow of a polytropic gas with time-fractional derivative. Comparisons are made between the considered techniques and also between their results. The obtained results reveal that these techniques are very simple and effective and give the solution in series form which in closed form gives the exact solution also, reveal that the integral iterative technique is simpler and shorter in its computational procedures and time than the other techniques.

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Solution of the System of Ordinary Differential Equations by Combined Laplace Transform–Adomian Decomposition Method

Cited by 16 publications

References 7 publications

A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution

A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution

Series Solution of Modelling the Pollution

Analytical techniques for solving the equation governing the unsteady flow of a polytropic gas with time-fractional derivative

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