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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.

MSC:
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
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