Detailed Error Analysis for a Fractional Adams Method View Full Text


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Article Info

DATE

2004-05

AUTHORS

Kai Diethelm, Neville J. Ford, Alan D. Freed

ABSTRACT

We investigate a method for the numerical solution of the nonlinear fractional differential equation D*αy(t)=f(t,y(t)), equipped with initial conditions y(k)(0)=y0(k), k=0,1,...,⌈α⌉−1. Here α may be an arbitrary positive real number, and the differential operator is the Caputo derivative. The numerical method can be seen as a generalization of the classical one-step Adams–Bashforth–Moulton scheme for first-order equations. We give a detailed error analysis for this algorithm. This includes, in particular, error bounds under various types of assumptions on the equation. Asymptotic expansions for the error are also mentioned briefly. The latter may be used in connection with Richardson's extrapolation principle to obtain modified versions of the algorithm that exhibit faster convergence behaviour. More... »

PAGES

31-52

References to SciGraph publications

  • 2002-09. Numerical Solution of the Bagley-Torvik Equation in BIT NUMERICAL MATHEMATICS
  • 1999. On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity in SCIENTIFIC COMPUTING IN CHEMICAL ENGINEERING II
  • 1971-12. A new dissipation model based on memory mechanism in PURE AND APPLIED GEOPHYSICS
  • 1997. Fractional Calculus in FRACTALS AND FRACTIONAL CALCULUS IN CONTINUUM MECHANICS
  • 1997. Fractional Calculus in FRACTALS AND FRACTIONAL CALCULUS IN CONTINUUM MECHANICS
  • 1971-04. Linear models of dissipation in anelastic solids in LA RIVISTA DEL NUOVO CIMENTO (1971-1977)
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    http://scigraph.springernature.com/pub.10.1023/b:numa.0000027736.85078.be

    DOI

    http://dx.doi.org/10.1023/b:numa.0000027736.85078.be

    DIMENSIONS

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