Abstract
The paper describes, in not too complicated cases, methods for the inclusion of unknown solutions mostly of (linear and nonlinear) differential equations, integral equations and some special types of functional equations. These methods are based on monotonicity principles and functional-analytic fixed point theorems and are often the only possible methods which give bounds for the absolute value of the error one can guarantee. Especially certain types of singular boundary value problems are considered, for instance point- and line-singularities in two and in three dimensions.
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Collatz, L. (1988). Inclusion of Solutions of Some Singular Boundary Value Problems in Two and Three Dimensions. In: Agarwal, R.P., Chow, Y.M., Wilson, S.J. (eds) Numerical Mathematics Singapore 1988. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 86. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6303-2_10
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DOI: https://doi.org/10.1007/978-3-0348-6303-2_10
Publisher Name: Birkhäuser, Basel
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