A predictor-corrector approach for the numerical solution of fractional differential equations. (English) Zbl 1009.65049

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

Nonlinear Dyn. 29, No. 1-4, 3-22 (2002).

Summary: We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05	Numerical methods for initial value problems
26A33	Fractional derivatives and integrals
34A34	Nonlinear ordinary differential equations and systems, general theory

Keywords:

fractional differential equation; Caputo derivative; predictor-corrector method; Adams method