High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

作者：Baffet Daniel^*; Hesthaven Jan S

来源：Journal of Scientific Computing, 2017, 72(3): 1169-1195.

DOI：10.1007/s10915-017-0393-z

• Fractional differential equations
• Volterra equations
• Kernel compression
• High-order numerical methods
• Integral deferred correction
• Local schemes

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel compression scheme for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our study on 1-step methods and approximate the local part of the fractional integral by integral deferred correction to enable high order accuracy. We study the local truncation error of integral deferred correction schemes for Volterra equations and present numerical results obtained with both implicit and the explicit methods applied to different problems.

• 出版日期2017-9