Abstract
There are boundary value problems with unbounded domains for which it is better to approximate the wanted solution by rational functions than by polynomials. Sometimes it may be necessary to use even more complicated approximations, for instance algebraic approximations. In simple cases it is possible to give guaranteeable inclusions for the solutions if monotonicity principles are valued. Some numerical examples are given.
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References
L. Collatz (1981): Anwendung von Monotoniesätzen zur Einschliessung der Lösungen von Gleichungen. Jahrbuch Überblicke der Mathem., 189–225.
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© 1989 Birkhäuser Verlag Basel
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Collatz, L. (1989). Rational and Algebraic Approximation for Initial- and Boundary-Value-Problems. In: Multivariate Approximation Theory IV. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7298-0_11
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DOI: https://doi.org/10.1007/978-3-0348-7298-0_11
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7300-0
Online ISBN: 978-3-0348-7298-0
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