Numerical analysis: an introduction
Numerical analysis: an introduction
Numerical integration of functions with poles near the interval of integration
Journal of Computational and Applied Mathematics
Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation
Communications of the ACM
Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives
Journal of Computational and Applied Mathematics
Uniform approximation to fractional derivatives of functions of algebraic singularity
Journal of Computational and Applied Mathematics
Some recent advances in theory and simulation of fractional diffusion processes
Journal of Computational and Applied Mathematics
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The fractional derivative D^qf(s) (0@?s@?1) of a given function f(s) with a positive non-integer q is defined in terms of an indefinite integral. We propose a uniform approximation scheme to D^qf(s) for algebraically singular functions f(s)=s^@ag(s) (@a-1) with smooth functions g(s). The present method consists of interpolating g(s) at sample points t"j in [0,1] by a finite sum of the Chebyshev polynomials. We demonstrate that for the non-negative integer m such that m=q-m-1. Some numerical examples in the simplest case 1