A new approach to shooting methods for terminal value problems of fractional differential equations

03/07/2023

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by   Kai Diethelm, et al.

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For terminal value problems of fractional differential equations of order α∈ (0,1), shooting methods that use Caputo derivatives are a well developed and investigated approach. Based on recently established analytic properties of such problems, we develop a new technique to select initial values that solve such shooting problems quickly and accurately. Numerical experiments indicate that this new technique, called proportional secting, converges accurately to the solution in very few iterations. Run time measurements indicate a speedup factor typically in the range between 4 and 10 in comparison to the often suggested standard bisection method.