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A New Approach to Shooting Methods for Terminal Value Problems of Fractional Differential Equations

  • 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.

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Metadaten
Author:Kai Diethelm, Frank Uhlig
Persistent identifier:http://doi.org/10.1007/s10915-023-02361-9
ISSN:0885-7474
Parent Title (English):Journal of Scientific Computing
Document Type:Article
Language:English
Year of publication:2023
Publishing Institution:Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt
Release Date:2023/10/04
Tag:Caputo derivative; Fractional differential equation; Proportional secting; Secant method; Shooting method; Terminal condition; Terminal value problem
Volume:97
Issue:2
Institutes and faculty:Fakultäten / Fakultät für angewandte Natur- und Geisteswissenschaften
Open access colour:Hybrid
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