High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations
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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.
KeywordsFractional differential equations Volterra equations Kernel compression High-order numerical methods Integral deferred correction Local schemes
The authors are grateful to Stefano Guarino for his contribution. Funding was provided by EPFL.
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