Short memory principle and a predictor–corrector approach for fractional differential equations
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摘要
Fractional differential equations are increasingly used to model problems in acoustics and thermal systems, rheology and modelling of materials and mechanical systems, signal processing and systems identification, control and robotics, and other areas of application. This paper further analyses the underlying structure of fractional differential equations. From a new point of view, we apprehend the short memory principle of fractional calculus and farther apply a Adams-type predictor–corrector approach for the numerical solution of fractional differential equation. And the detailed error analysis is presented. Combining the short memory principle and the predictor–corrector approach, we gain a good numerical approximation of the true solution of fractional differential equation at reasonable computational cost. A numerical example is provided and compared with the exact analytical solution for illustrating the effectiveness of the short memory principle.
论文关键词:26A33,65D05,65D30,Fractional differential equation,Caputo derivative,Short memory principle,Numerical solution,Predictor–corrector method
论文评审过程:Received 28 April 2006, Available online 24 July 2006.
论文官网地址:https://doi.org/10.1016/j.cam.2006.06.008