A matrix method for fractional Sturm-Liouville problems on bounded domain

被引：0
作者：
Paolo Ghelardoni
Cecilia Magherini
机构：
[1] Università di Pisa,Dipartimento di Matematica
来源：
Advances in Computational Mathematics | 2017年 / 43卷
关键词：
Fractional Sturm-Liouville eigenproblems; Quantum Riesz derivative; Matrix method; Orthogonal polynomials; 65L15; 65L20; 34A08; 33C45;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A matrix method for the solution of direct fractional Sturm-Liouville problems (SLPs) on bounded domains is proposed where the fractional derivative is defined in the Riesz sense. The scheme is based on the application of the Galerkin spectral method of orthogonal polynomials. The order of convergence of the eigenvalue approximations with respect to the matrix size is studied. Some numerical examples that confirm the theory and prove the competitiveness of the approach are finally presented.
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页码：1377 / 1401
页数：24
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共 35 条
  • [1] Bañuelos R(2004)The Cauchy process and the Steklov problem J. Funct. Anal. 211 355-423
  • [2] Kulczycki T(1987)An extension od Aronszajn’s rule: slicing the spectrum for intermediate problems, SIAM J. Numer. Anal. 24 828-843
  • [3] Beattie C(2012)Crank-nicolson method for the fractional diffusion equation with the Riesz fractional derivative J. Comput. Phys. 231 1743-1750
  • [4] Çelik C(2005)Two-sided eigenvalue estimates for subordinate processes in domains J. Funct. Anal. 226 90-113
  • [5] Duman M(2004)Higher order PDEs and symmetric stable processes Probab. Theory Related Fields 129 495-536
  • [6] Chen ZQ(2015)Computing the Ground and First Excited States of the Fractional schrödinger Equation in an Infinite Potential Well Commun. Comput. Phys. 18 321-350
  • [7] Song R(1969)Calculation of Gauss quadrature rules Math. Comp. 23 221-230
  • [8] DeBlassie RD(2015)On the numerical solution of the eigenvalue problem in fractional quantum mechanics Commun. Nonlinear Sci. Numer. Simul. 20 604-613
  • [9] Duo S(2011)A fast and simple algorithm for the computation of Legendre coefficients Numer. Math. 117 529-553
  • [10] Zhang Y(2011)Spectral analysis of subordinate Brownian motions on the half-line Studia Math. 206 211-271
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