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Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models
المؤلفون المشاركون
Chu, Yu-Ming
Ahmad, Hijaz
Khan, Tufail A.
Ahmad, Imtiaz
Stanimirović, Predrag S.
المصدر
العدد
المجلد 2020، العدد 2020 (31 ديسمبر/كانون الأول 2020)، ص ص. 1-14، 14ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2020-10-06
دولة النشر
مصر
عدد الصفحات
14
التخصصات الرئيسية
الملخص EN
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.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Ahmad, Hijaz& Khan, Tufail A.& Stanimirović, Predrag S.& Chu, Yu-Ming& Ahmad, Imtiaz. 2020. Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models. Complexity،Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1144812
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Ahmad, Hijaz…[et al.]. Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models. Complexity No. 2020 (2020), pp.1-14.
https://search.emarefa.net/detail/BIM-1144812
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Ahmad, Hijaz& Khan, Tufail A.& Stanimirović, Predrag S.& Chu, Yu-Ming& Ahmad, Imtiaz. Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models. Complexity. 2020. Vol. 2020, no. 2020, pp.1-14.
https://search.emarefa.net/detail/BIM-1144812
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1144812
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