Stable fractional Chebyshev differentiation matrix for the numerical solution of multi-order fractional differential equations
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DOI: 10.1007/s11071-017-3654-3
Abstract: This paper presents an algorithm to obtain numerically stable differentiation matrices for approximating the left- and right-sided Caputo-fractional derivatives. The proposed differentiation matrices named fractional Chebyshev differentiation matrices are obtained using stable recurrence relations at… read more here.
Keywords: order; chebyshev differentiation; differentiation; differentiation matrices ... See more keywords
Differentiation matrices for univariate polynomials
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DOI: 10.1007/s11075-019-00668-z
Abstract: Differentiation matrices are in wide use in numerical algorithms, although usually studied in an ad hoc manner. We collect here in this review paper elementary properties of differentiation matrices for univariate polynomials expressed in various… read more here.
Keywords: differentiation matrices; univariate polynomials; differentiation; matrices univariate ... See more keywords
Fractional spectral differentiation matrices based on Legendre approximation
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DOI: 10.1186/s13662-020-02590-4
Abstract: A simple scheme is proposed for computing N × N $N \times N$ spectral differentiation matrices of fractional order α for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous… read more here.
Keywords: legendre approximation; fractional spectral; differentiation matrices; spectral differentiation ... See more keywords