Refine
Year of publication
Document Type
- Article (76)
- Conference Proceeding (10)
- Part of a Book (7)
- Book (4)
- Preprint (4)
- Doctoral Thesis (1)
Keywords
- fractional calculus (3)
- Caputo derivative (2)
- Fractional differential equation (1)
- Proportional secting (1)
- Riemann-Liouville derivative (1)
- Riemann-Liouville integral (1)
- Secant method (1)
- Shooting method (1)
- Terminal condition (1)
- Terminal value problem (1)
- Wahlverfahren (1)
- asymptotic behaviour of solutions (1)
- dengue fever (1)
- differential equations (1)
- disease simulation (1)
- fractional derivative (1)
- fractional differential equation (1)
- mathematical model (1)
- non-commensurate fractional order planar systems (1)
- numerical analysis (1)
- numerical method (1)
We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples.
A New Approach to Shooting Methods for Terminal Value Problems of Fractional Differential Equations
(2023)
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.