Fractional Spectral Differentiation Matrices Based on Legendre Approximation
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Abstract
A simple scheme is proposed for computing NxN spectral differentiation matrices of fractional order alpha for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous three-term recurrence relation and is numerically stable. The matrices are then applied to numerically differentiate.
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Keywords
Fractional Spectral Differentiation Matrices, Fractional Calculus, Legendre Polynomials, Numerical Differentiation, Mathematical analysis, Quantum mechanics, Term (time), Differential equation, Numerical Integration Methods for Differential Equations, QA1-939, FOS: Mathematics, Homogeneous, Fractional spectral differentiation matrices, Anomalous Diffusion Modeling and Analysis, Matrix Algorithms and Iterative Methods, Numerical Analysis, Time-Fractional Diffusion Equation, Physics, Fractional calculus, Numerical Linear Algebra, Partial differential equation, Applied mathematics, Fractional Derivatives, Numerical differentiation, Computational Theory and Mathematics, Combinatorics, Modeling and Simulation, Physical Sciences, Computer Science, Legendre polynomials, Fractional Calculus, Mathematics, Ordinary differential equation, Matrix Computations, fractional spectral differentiation matrices, Fractional ordinary differential equations, fractional calculus, Numerical methods for initial value problems involving ordinary differential equations, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Fractional derivatives and integrals, numerical differentiation
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01 natural sciences, 0103 physical sciences
Citation
Ghorbani, Asghar; Baleanu, Dumitru (2020). "Fractional spectral differentiation matrices based on Legendre approximation", Advances in Difference Equations, Vol. 2020, No. 1.
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6
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2020
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1
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Scopus : 7
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