TY - JOUR A1 - Diethelm, Kai A1 - Uhlig, Frank T1 - A New Approach to Shooting Methods for Terminal Value Problems of Fractional Differential Equations T2 - Journal of Scientific Computing N2 - For terminal value problems of fractional differential equations of order α∈(0,1) that use Caputo derivatives, shooting methods are a well developed and investigated approach. Based on recently established analytic properties of such problems, we develop a new technique to select the required initial values that solves such shooting problems quickly and accurately. Numerical experiments indicate that this new proportional secting technique converges very quickly and accurately to the solution. Run time measurements indicate a speedup factor of between 4 and 10 when compared to the standard bisection method. KW - Fractional differential equation KW - Caputo derivative KW - Terminal condition KW - Terminal value problem KW - Shooting method KW - Proportional secting KW - Secant method Y1 - 2023 UR - https://opus4.kobv.de/opus4-fhws/frontdoor/index/index/docId/4396 UR - doi.org/10.1007/s10915-023-02361-9 SN - 0885-7474 VL - 97 IS - 2 ER -