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Abstract
In this paper we present an overview of analytical results and numerical methods for singular boundary value problems for ordinary differential equations with a singularity of the first kind. Special attention is paid to the analysis of shooting methods, where the associated initial value problems are solved by the acceleration technique known as Iterated Defect Correction (IDeC) based on the backward Euler method, and on direct discretization using collocation schemes. Convergence, error estimation and mesh selection are discussed for both approaches. Moreover, we study the fixed point convergence of the IDeC iteration, where the fixed point corresponds to a collocation solution.
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Authors and Affiliations
Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria
Winfried Auzinger, Othmar Koch & Ewa Weinmüller
- Winfried Auzinger
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- Othmar Koch
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- Ewa Weinmüller
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Editors and Affiliations
Institute of Mathematics and Computer Science, Technical University of Czestochowa, Dabrowskiego 73, 42-200, Czestochowa, Poland
Roman Wyrzykowski
Computer Science Department, University of Tennessee, 122 Volunteer Blvd, Knoxville, TN, 37996-3450, USA
Jack Dongarra
Computer Science Department, Oklahoma State University, 700 N. Greenwood Ave., Tulsa, OK, 74106, USA
Marcin Paprzycki
DTU, UNI-C, Danish Computing Centre for Research and Education, Bldg. 304, 2800, Lyngby, Denmark
Jerzy Waśniewski
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© 2002 Springer-Verlag Berlin Heidelberg
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Auzinger, W., Koch, O., Weinmüller, E. (2002). Theory and Solution Techniques for Singular Boundary Value Problems in Ordinary Differential Equations. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_95
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