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مقالات فارسیISIکنفرانسهاژورنالها

Modal spectral Tchebyshev Petrov–Galerkin stratagem for the time-fractional nonlinear Burgers’ equation

محل انتشار: مجله ایرانی آنالیز عددی و بهینه سازی، دوره: 14، شماره: 28
سال انتشار: 1403
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 55

فایل این مقاله در 29 صفحه با فرمت PDF قابل دریافت می باشد

استخراج به نرم افزارهای پژوهشی:

لینک ثابت به این مقاله:
https://civilica.com/doc/1903076

شناسه ملی سند علمی:

JR_IJNAO-14-28_007

تاریخ نمایه سازی: 16 بهمن 1402

چکیده مقاله:

Herein, we construct an explicit modal numerical solver based on the spec-tral Petrov–Galerkin method via a specific combination of shifted Cheby-shev polynomial basis for handling the nonlinear time-fractional Burger-type partial differential equation in the Caputo sense. The process reduces the problem to a nonlinear system of algebraic equations. Solving this alge-braic equation system will yield the approximate solution’s unknown coef-ficients. Many relevant properties of Chebyshev polynomials are reported, some connection and linearization formulas are reported and proved, and all elements of the obtained matrices are evaluated neatly. Also, conver-gence and error analyses are established. Various illustrative examples demonstrate the applicability and accuracy of the proposed method and depict the absolute and estimated error figures. Besides, the current ap-proach’s high efficiency is proved by comparing it with other techniques in the literature.

کلیدواژه ها:

Time-fractional Burgers’ equation ، Chebyshev polynomials ، Petrov–Galerkin method ، Convergence Analysis

نویسندگان

Y.H. Youssri

Department of Mathematics, Faculty of Science, Cairo University, Giza ۱۲۶۱۳, Egypt.

A.G. Atta

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo ۱۱۳۴۱, Egypt.

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