Rigorous integration of non-linear ordinary differential equations in Chebyshev basis. (English) Zbl 1325.65101

This paper shows how to compute enclosures for the solution of initial value problems using Chebyshev expansions rather than a Taylor-like approach. The method relies on the development of an algorithm that computes the multiplication of two function enclosures in truncated Chebyshev form. A Picard-type iteration scheme is used to obtain the enclosures and in order to integrate over larger time windows, then several steps of integration are needed in which the so-called wrapping effect can be suppressed. The approach seems to allow for higher precision with lower-order approximations than in the Taylor model. However, there are still issues with stiffness and even modest sized systems that this work does not address.


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
Full Text: DOI


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