Numerical differentiation of implicitly defined space curves

DOI10.1007/BF02259095zbMath0666.65016MaRDI QIDQ1116639

Wolfgang Mackens

Publication date: 1989

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

finite difference methodnumerical examplesbifurcationderivativesreduced basis methodpredictor-corrector branch followingregular solution curves

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical differentiation (65D25)

Related Items

Design and evaluation of homotopies for efficient and robust continuation ⋮ Efficient numerical differentiation of implicitly-defined curves for sparse systems ⋮ Monolithic homotopy continuation with predictor based on higher derivatives ⋮ On the theory and error estimation of the reduced basis method for multi-parameter problems ⋮ Path-following methods in bifurcation problems ⋮ On the Reduced Basis Method ⋮ On the Reduced Basis Method ⋮ Robust continuation methods for tracing solution curves of parameterized systems ⋮ Mixed precision path tracking for polynomial homotopy continuation ⋮ Conjugate gradient predictor corrector method for solving large scale problems ⋮ The modified Broyden-variational method for solving nonlinear elliptic differential equations ⋮ Numerical differentiation of implicitly defined curves

Cites Work

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• A stepsize control for continuation methods and its special application to multiple shooting techniques
• Über einen Ordnungsbegriff bei Einbettungsalgorithmen zur Lösung nichtlinearer Gleichungen
• On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations
• Estimation of the Error in the Reduced Basis Method Solution of Nonlinear Equations
• Higher Order Predictors and Adaptive Steplength Control in Path Following Algorithms
• Solution Fields of Nonlinear Equations and Continuation Methods
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations

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