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 involving ordinary differential equations
26A33	Fractional derivatives and integrals
34A34	Nonlinear ordinary differential equations and systems

Keywords:

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