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.
Journal of Scientific Computing – Springer Journals
Published: Feb 20, 2017
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