Diethelm, Kai; Ford, Neville J.; Freed, Alan D. Detailed error analysis for a fractional Adams method. (English) Zbl 1055.65098 Numer. Algorithms 36, No. 1, 31-52 (2004). The authors use the equivalent Volterra integral equation to derive a generalization of the Adams-Bashforth/Moulton method for a fractional differential equation. They provide an error analysis and give a numerical example. Reviewer: J. D. P. Donnelly (Oxford) Cited in 4 ReviewsCited in 398 Documents MSC: 65L70 Error bounds for numerical methods for ordinary differential equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 26A33 Fractional derivatives and integrals 65L20 Stability and convergence of numerical methods for ordinary differential equations 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:fractional differential equation; Caputo derivative; Adams-Bashforth-Moulton method; numerical example PDFBibTeX XMLCite \textit{K. Diethelm} et al., Numer. Algorithms 36, No. 1, 31--52 (2004; Zbl 1055.65098) Full Text: DOI