Adaptive Piecewise Poly-Sinc Methods for Ordinary Differential Equations
- Resource Type
- article
- Authors
- Omar Khalil; Hany El-Sharkawy; Maha Youssef; Gerd Baumann
- Source
- Algorithms, Vol 15, Iss 9, p 320 (2022)
- Subject
- adaptive approximation
Poly-Sinc interpolation
Sinc methods
Lagrange interpolation
initial value problems
boundary value problems
Industrial engineering. Management engineering
T55.4-60.8
Electronic computers. Computer science
QA75.5-76.95
- Language
- English
- ISSN
- 1999-4893
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the adaptive piecewise Poly-Sinc method to function approximation, for which we derived an a priori error estimate for our adaptive method and showed its exponential convergence in the number of iterations. In this work, we show the exponential convergence in the number of iterations of the a priori error estimate obtained from the piecewise collocation method, provided that a good estimate of the exact solution of the ordinary differential equation at the Sinc points exists. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary differential equations.