Analytic approximate solutions of diffusion equations arising in oil pollution

Ahmad, Harith; Khan, Tufail A.; Durur, Hülya; Ismail, Gamal; Yokuş, Asıf

doi:10.1016/j.joes.2020.05.002

Cited by 41 publications

(24 citation statements)

References 37 publications

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“…√√ √√ � 0 and p and λ(ϑ) are the auxiliary parameter and Lagrange multiplier, respectively, which can be found optimally. e first one is used to accelerate the convergence to the exact solution [39][40][41][42][43], while the second one is used to construct the correction function [44]. e significant value of λ(ϑ) can be achieved by applying δ on both the sides of the recurrent relation (4) with respect to Z n (ξ), which leads to…”

Section: Modified Iteration Algorithm-iimentioning

confidence: 99%

Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

et al. 2020

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Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.

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Section: Modified Iteration Algorithm-iimentioning

confidence: 99%

Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

et al. 2020

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“…GG  -expansion method [11,12], Adomian's decomposition method [13], collocation method [14,15], sub equation method [16,17], Homotopy perturbation method [18], new sub equation method [19] and so on [28][29][30][31][32][33][34][35].…”

Section:  mentioning

confidence: 99%

Düzenli Uzun Dalga Denkleminin Hiperbolik Tip Yürüyen Dalga Çözümleri

Durur

Yokuş

Kaya

2020

Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi

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Bu çalışmanın temel amacı   1 G -açılım yöntemi kullanılarak Düzenli Uzun Dalga (RLW) denklemi için yürüyen dalga çözümlerini elde etmektir. Elde edilen çözümlerde sabitlere özel değerler verilerek 3 boyutlu, 2 boyutlu ve kontur grafikleri sunulmuştur. Bu grafikler Düzenli Uzun Dalga denkleminin özel bir çözümüdür ve denklemin durağan bir dalgasını temsil etmektedir. Bu makalede sunulan çözümleri ve grafikleri bulmak için bilgisayar paket programı kullanılmaktadır.

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“…Turkyilmazoglu [3] presented the modication in variational iteration scheme by introducing the concept of accelerating convergence parameter. Oil diusion model was studied by Ahmad et al [4]. They presented the analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Novel Schemes for Cauchy-Riemann System of Equations with Cauchy Conditions

Naseem

Sohail

Zeb

2021

Advances in the Theory of Nonlinear Analysis and Its Application

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This communication deals with the analytical solutions of Cauchy problem for Cauchy-Riemann system of equations which is basically unstable according to Hadamard but its solution exists if its initial data is analytic. Here, we used the Vectorial Adomian Decomposition (VAD) method, Vectorial Variational Iteration (VVI) method, and Vectorial Modied Picard's Method (VMP) method to get the convergent series solution.These suggested schemes give analytical approximation in an innite series form without using discretization.These methods are eectual and reliable which is demonstrated through six model problems having variety of source terms and analytic initial data.

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Analytic approximate solutions of diffusion equations arising in oil pollution

Cited by 41 publications

References 37 publications

Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Düzenli Uzun Dalga Denkleminin Hiperbolik Tip Yürüyen Dalga Çözümleri

Novel Schemes for Cauchy-Riemann System of Equations with Cauchy Conditions

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