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Numerical Treatment of Countable Systems of Ordinary Differential Equations.

Please always quote using this URN: urn:nbn:de:0297-zib-4728
  • 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.

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Author:Michael Wulkow
Document Type:ZIB-Report
Date of first Publication:1990/11/26
Series (Serial Number):ZIB-Report (TR-90-08)
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