On linear stability of predictor–corrector algorithms for fractional differential equations

Abstract

This paper deals with the numerical approximation of differential equations of fractional order by means of predictor–corrector algorithms. A linear stability analysis is performed and the stability regions of different methods are compared. Furthermore the effects on stability of multiple corrector iterations are verified.

Keywords:

• fractional differential equation
• predictor–corrector
• product integration rule
• stability

2000 AMS Subject Classifications :

• 65L06
• 65L20
• 26A33

Acknowledgements

The author is grateful to the anonymous referee whose valuable suggestions and comments helped in improving this paper.