کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6933565 | 867595 | 2013 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation
ترجمه فارسی عنوان
خصوصیات استروم-لیوویلر مضر: نظریه و تقریب عددی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
We first consider a regular fractional Sturm-Liouville problem of two kinds RFSLP-I and RFSLP-II of order νâ(0,2). The corresponding fractional differential operators in these problems are both of Riemann-Liouville and Caputo type, of the same fractional order μ=ν/2â(0,1). We obtain the analytical eigensolutions to RFSLP-I & -II as non-polynomial functions, which we define as Jacobi poly-fractonomials. These eigenfunctions are orthogonal with respect to the weight function associated with RFSLP-I & -II. Subsequently, we extend the fractional operators to a new family of singular fractional Sturm-Liouville problems of two kinds, SFSLP-I and SFSLP-II. We show that the primary regular boundary-value problems RFSLP-I & -II are indeed asymptotic cases for the singular counterparts SFSLP-I & -II. Furthermore, we prove that the eigenvalues of the singular problems are real-valued and the corresponding eigenfunctions are orthogonal. In addition, we obtain the eigen-solutions to SFSLP-I & -II analytically, also as non-polynomial functions, hence completing the whole family of the Jacobi poly-fractonomials. In numerical examples, we employ the new poly-fractonomial bases to demonstrate the exponential convergence of the approximation in agreement with the theoretical results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 252, 1 November 2013, Pages 495-517
Journal: Journal of Computational Physics - Volume 252, 1 November 2013, Pages 495-517
نویسندگان
Mohsen Zayernouri, George Em Karniadakis,