A new algorithm for computing the differential transform in nonlinear two-dimensional partial differential equations

Elsaid, A.; Helal, S.M.

doi:10.1016/j.jksus.2019.04.004

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…Mirzaaghaian & Ganji (2016) examined the applicability of DTM to some physical problems such as heat transfer through permeable walls and micropolar fluid flow. Elsaid & Helal (2020) developed a new modification of the DTM to calculate partial derivatives of nonlinear functions of two variables. They also used a different algoritm that does not require any intermediate calculations, which eliminates some of the shortcomings of many previous algorithms (Elsaid & Helal, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…Elsaid & Helal (2020) developed a new modification of the DTM to calculate partial derivatives of nonlinear functions of two variables. They also used a different algoritm that does not require any intermediate calculations, which eliminates some of the shortcomings of many previous algorithms (Elsaid & Helal, 2020). Odibat et al (2008) adapted the classical DTM in such a way that it could be applied not only to ordinary and partial differential equations but also fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Parameterized Differential Transform Method and Its Application to Boundary Value Transmission Problems

Yücel

Muhtarov

2023

Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, we developed a new modification of the well-known differential transformation method (DTM) that differs from the classical one by the algorithm for calculating the coefficients of an approximate solution given as a series. The proposed new algorithm we will call α-parameterized DTM (α-P DTM,for short). By using the proposed α-DTM we solve the boundary value transmission problem for the 3rd order differential equation. For the same problem, an approximate solution is found using also the classical DTM. The solutions obtained were compared graphically.

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Section: Introductionmentioning

confidence: 99%