Abstract
New extendable LU sparse factorization procedures are presented for the solution of non-linear elliptic difference equations. The derived iterative methods are shown to be both competitive and computationally efficient in comparison with existing schemes. Application of the methods on non-linear elliptic boundary value problems both in two and three space dimensions are discussed and numerical results are given.
Zusammenfassung
Neue, erweiterte Verfahren der schwachbesetzten LU-Faktorisierung für die Lösung nichtlinearer elliptischer Differenzengleichungen werden vorgestellt. Von den zugehörigen Iterationsverfahren wird gezeigt, daß sie im Vergleich mit bekannten Verfahren konkurrenzfähig und numerisch effizient sind. Die Anwendung der Methoden auf nichtlineare elliptische Randwertprobleme in zwei und drei Dimensionen wird diskutiert; numerische Ergebnisse werden angegeben.
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Lipitakis, E.A., Evans, D.J. Solving non-linear elliptic difference equations by extendable sparse factorization procedures. Computing 24, 325–339 (1980). https://doi.org/10.1007/BF02237818
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DOI: https://doi.org/10.1007/BF02237818
Key words and phrases
- Non-linear equations
- Elliptic partial differential equations
- Solution of linear systems
- Factorization
- Three space dimensions