کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6929964 867655 2016 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spectral approximation methods and error estimates for Caputo fractional derivative with applications to initial-value problems
ترجمه فارسی عنوان
روش تقریبی طیفی و برآورد خطا برای مشتق تقسیم کاپتو با برنامه های کاربردی به مشکلات اولیه ارزش
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
In this paper, we revisit two spectral approximations, including truncated approximation and interpolation for Caputo fractional derivative. The two approaches have been studied to approximate Riemann-Liouville (R-L) fractional derivative by Chen et al. and Zayernouri et al. respectively in their most recent work. For truncated approximation the reconsideration partly arises from the difference between fractional derivative in R-L sense and Caputo sense: Caputo fractional derivative requires higher regularity of the unknown than R-L version. Another reason for the reconsideration is that we distinguish the differential order of the unknown with the index of Jacobi polynomials, which is not presented in the previous work. Also we provide a way to choose the index when facing multi-order problems. By using generalized Hardy's inequality, the gap between the weighted Sobolev space involving Caputo fractional derivative and the classical weighted space is bridged, then the optimal projection error is derived in the non-uniformly Jacobi-weighted Sobolev space and the maximum absolute error is presented as well. For the interpolation, analysis of interpolation error was not given in their work. In this paper we build the interpolation error in non-uniformly Jacobi-weighted Sobolev space by constructing fractional inverse inequality. With combining collocation method, the approximation technique is applied to solve fractional initial-value problems (FIVPs). Numerical examples are also provided to illustrate the effectiveness of this algorithm.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 319, 15 August 2016, Pages 108-128
نویسندگان
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