High-order accurate local schemes for fractional differential equations
High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional dierential equations. The schemes are based on an expansion in a weighted L2 space. To obtain the schemes this expansion is terminated after P +1 terms. We study the local truncation error and its behavior with respect to the step-size h and and P. Building on this analysis, we develop an error indicator, based on the Milne device. Methods with xed and variable step-size are tested numerically on a number of problems, including problems with known solutions, and a fractional version on the Van der Pol equation.
Record created on 2014-12-19, modified on 2016-08-09