472
eng
reportzib
0
1990-11-26
1990-11-26
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Numerical Treatment of Countable Systems of Ordinary Differential Equations.
Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and medicine. They can be considered as ordinary differential equations in sequence spaces. In this work, a full adaptive algorithm for the computational treatment of such systems is developed. The method combines time discretization with extrapolation in Hilbert spaces with a discrete Galerkin approach as discretization of the stationary subproblems. The Galerkin method is based on orthogonal functions of a discrete variable , which are generated by certain weight functions. A theory of countable systems in the associated weighted sequence spaces is developed as well as a theory of the Galerkin method. The Galerkin equations can be assembled either by use of analytical properties of the orthogonal functions or numerically by a multilevel summation algorithm. The resulting algorithm CODEX is applied to many examples of technological interest, in particular from polymer chemistry.
TR-90-08
472
urn:nbn:de:0297-zib-4728
Michael Wulkow
ZIB-Report
TR-90-08
Informatik, Informationswissenschaft, allgemeine Werke
ZIB Allgemein
Wulkow, Michael
https://opus4.kobv.de/opus4-zib/files/472/TR-90-08.pdf