×

Evaluation of the solution of an integral-functional equation. (English) Zbl 1070.65140

The author considers the solution of a homogeneous integral-functional equation under the assumption that the solution is an arbitrarily often differentiable and compactly supported function. Algorithms for the evaluation of that solution are given.

MSC:

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Berg, L.; Krüppel, M., On the solution of an integral-functional equation with a parameter, J. Anal. Appl., 17, 159-181 (1998) · Zbl 0897.45004
[2] Berg, L.; Krüppel, M., Cantor sets and integral-functional equations, J. Anal. Appl., 17, 997-1020 (1998) · Zbl 0926.45002
[3] Berg, L.; Krüppel, M., Series expansions for the solution of an integral-functional equation with a parameter, Resultate Math., 41, 213-228 (2002) · Zbl 1032.45001
[4] Henrici, P., Elemente der numerischen Analysis, Bd. 1 (1972), Bibliographisches Institut: Bibliographisches Institut Mannheim · Zbl 0229.65002
[5] Kress, R., Numerical Analysis (1998), Springer: Springer New York · Zbl 0913.65001
[6] Pollen, D., Daubechies’ scaling function on \([0, 3]\), (Chui, C. K., Wavelets—A Tutorial in Theory and Applications (1992), Academic Press: Academic Press San Diego), 3-13 · Zbl 0760.42017
[7] Rvachev, V. A., Compactly supported solutions of functional-differential equations and their applications, Russian Math. Surveys, 45, 87-120 (1990) · Zbl 0704.34090
[8] Schnabl, R., Über eine \(C^\infty \)-Funktion, Lecture Notes in Math., 1114, 134-142 (1985) · Zbl 0567.41027
[9] Strang, G., Wavelets and dilation equationsA brief introduction, SIAM Rev., 31, 614-627 (1989) · Zbl 0683.42030
[10] Volk, W., Properties of subspaces generated by an infinitely often differentiable function and its translates, ZAMM Z. Angew. Math. Mech., 76, Suppl. 1, 575-576 (1996) · Zbl 0900.41012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.