A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques

DOI10.1007/BF01395950zbMath0335.65033OpenAlexW2058662980MaRDI QIDQ1229559

Peter Rentrop, Hans Josef Pesch, Peter Deuflhard

Publication date: 1976

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132418

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

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Cites Work

• Optimization and optimal control. Proceedings of a conference held at Oberwolfach, November 17-23, 1974
• A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
• Numerical solution of the singular Ginzburg-Landau equations by multiple shooting
• A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques
• Numerical calculation of elliptic integrals and elliptic functions
• Numerische Aspekte bei der Einbettung nichtlinearer Probleme
• Automatische Schrittweitensteuerung bei global konvergenten Einbettungsmethoden
• On the Stability Problem for Shallow Spherical Shells
• Local Mapping Relations and Global Implicit Function Theorems
• Numerical solution of nonlinear two-point boundary problems by finite difference methods
• The continuation method for functional equations
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