An Efficient Method for Solving Linear and Nonlinear System of Partial Differential Equations

Mahgoub, Mohand M. Abdelrahim; Sedeeg, Abdelilah Kamal H.

doi:10.9734/bjmcs/2017/30259

Cited by 4 publications

(4 citation statements)

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“…This applying work got its motivation from created by Akinola [25] and thusly broadly figured out how the higher solicitation issues considered are being changed by Aboodh Transformation and its reverse ([26] - [28]), how Series Method is being used to manage the sensational abilities [29]. The results got by the mix of the three referred to procedures have shown the strength of Aboodh Transform Series Decomposition Method (ATSDM) to the extent that practicality, precision, and immovable quality over any leftover strategies differentiated and.…”

Section: Methodology Of Aboodh Transformationmentioning

confidence: 99%

Computational method and dissipative feature for solving a network SIRS model

Mahdy

Amer

Youssef³

2023

Bulletin of Faculty of Science, Zagazig University

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In this research, we have introduced the new organization model for SIRS. The model has portrayed occasional flu. We have talked about the dissipative element for the SIRS model, the powerful ways of behaving of the vulnerable tainted helpless (SIS) model, the defenseless contaminated recuperated (SIR) model, and the helpless tainted recuperated helpless (SIRS) model have generally concentrated on complex organizations. The model has portrayed the outline by the sign stream. We have given the Aboodh change series decay strategy (ATSDM). Likewise, move toward arrangements of the nonlinear model for SIRS were obtained through ATSDM: a method planned to find the indispensable and the backwards change of the difficulties, increase the remarkable capability, and at a comparative time, decay the nonlinear condition. We have settled the SIRS model by utilizing (ATSDM). We are showing the outcomes with various introductory circumstances. The results gained from all the layouts considered are, with no trace of vulnerability, a verification of how ATSDM is an astonishing and accepted harsh method that any expert can use in getting a precise delayed consequence of any issue of the sort contemplated here in this ongoing work.

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Section: Methodology Of Aboodh Transformationmentioning

confidence: 99%

Computational method and dissipative feature for solving a network SIRS model

Mahdy

Amer

Youssef³

2023

Bulletin of Faculty of Science, Zagazig University

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“…(2) was obtained by applying the Aboodh Transform on Eq. (1) (Aboodh, 2013(Aboodh, , 2014Abdelbagy & Mohand, 2016;Mahgoub & Sedeeg, 2017):…”

Section: 𝐿𝑢(𝑥) + 𝑅𝑢(𝑥) + 𝑁𝑢(𝑥) = 𝑔(𝑥)mentioning

confidence: 99%

“…Consequently, researchers have devised an alternative approach for obtaining an approximate solution in the literature (Oderinu, 2014;Opanuga et al, 2015Opanuga et al, , 2017Akinola et al, 2017;Noor & Mohyud-Din, 2008;Hymavathi & Kumar, 2014;Mohyud-din, 2009;Siddiqi et al, 2009;El-Gamel, 2015;Owolabi et al, 2019;Adeyefa & Kuboye, 2020;Farooq et al, 2020;Gbadamosi et al, 2010;Amer et al, 2018;Gepreel et al, 2020;Mahdy, 2019;Mandy and Youssef, 2021). This research work derived its motivation from the work of Akinola et al (2016), and extensively explained how the higher order problems considered are being transformed by the Aboodh Transformation and its inverse (Aboodh 2013(Aboodh , 2014Abdelbagy & Mohand, 2016;Mahgoub & Sedeeg, 2017), how the Series Method is being employed to handle the exponential functions (Yalçinbaş, 2002), and how nonlinear terms are being decomposed by the means of Adomian Polynomials (Adomian, 1988;Abbaoui & Cherruault, 1994). The results obtained by the combination of the three mentioned methods have demonstrated the strength of the Aboodh Transform Series Decomposition Method (ATSDM) in terms of efficacy, accuracy and reliability over all other related methods available.…”

Section: Introductionmentioning

confidence: 99%

An Integral Transform Together With Taylor Series and Decomposition Method for the Solutiononlinear Boundary Value Problems of Higher Order

Akinola

Owolabi

Alao

et al. 2023

MJS

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This work aims to determine the approximate solutions of nonlinear boundary value problems of higher order obtained through the Aboodh Transform Series Decomposition Method (ATSDM), a method designed to find the integral and the inverse transform of the problems, expand the exponential function, and simultaneously decompose the nonlinear terms. The results obtained demonstrate that ATSDM is an excellent and trusted approximate method that can be employed to obtain accurate results for any problem similar to the one presented in this work.

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“…This transformation has deeper connection with the Laplace and Elzaki transform [8]. The coupling of Adomian decomposition method with Aboodh transform method has been applied for solving linear and nonlinear equations [17], to solve system of linear and nonlinear partial differential equations [13] and for solving time-fractional diffusion equation [16].…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

Cherif

Ziane

2017

ijaa

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Abstract. In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

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An Efficient Method for Solving Linear and Nonlinear System of Partial Differential Equations

Cited by 4 publications

References 0 publications

Computational method and dissipative feature for solving a network SIRS model

Computational method and dissipative feature for solving a network SIRS model

An Integral Transform Together With Taylor Series and Decomposition Method for the Solutiononlinear Boundary Value Problems of Higher Order

A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

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