Discretized Fractional Calculus
Copyright policy )Discretized Fractional Calculus
Es werden für Fraktionalintegrale der Form \(\int^{x}_{0}(x- s)^{\alpha -1}x^{\beta -1}g(x)ds\) Konvolutionsquadraturen untersucht, d.h. numerische Näherungen in den Punkten \(x=0,h,2h,...Nh\) bestimmt. Es wird gezeigt, daß die angegebenen Methoden konvergent von der Ordnung p sind, wenn sie stabil und von der Ordnung p konsistent sind. Schließlich werden einige numerische Beispiele und Anwendungen angegeben, wie die Behandlung der Abelschen Integralgleichung, das Diffusionsproblem (Wärmeleitung im Halbraum) und die Berechnung von speziellen Funktionen der mathematischen Physik.
Abel-Liouville integrals, discrete convolution, fractional integrals, fractional linear multistep methods, Numerical methods for integral equations, Numerical quadrature and cubature formulas, diffusion problems, Approximate quadratures, Euler's gamma function, Numerical differentiation, special functions, Computation of special functions and constants, construction of tables, Fractional derivatives and integrals, convolution quadratures, Riemann-Liouville integrals, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Gamma, beta and polygamma functions, Abel integral equations
Abel-Liouville integrals, discrete convolution, fractional integrals, fractional linear multistep methods, Numerical methods for integral equations, Numerical quadrature and cubature formulas, diffusion problems, Approximate quadratures, Euler's gamma function, Numerical differentiation, special functions, Computation of special functions and constants, construction of tables, Fractional derivatives and integrals, convolution quadratures, Riemann-Liouville integrals, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Gamma, beta and polygamma functions, Abel integral equations
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).782 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 0.1% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 0.1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!