Discrete Newton methods and iterated defect corrections

DOI10.1007/BF01398251zbMath0459.65035OpenAlexW2025550094MaRDI QIDQ1152204

Klaus Böhmer

Publication date: 1981

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

Full work available at URL: https://eudml.org/doc/132725

zbMATH Keywords

numerical resultsNewton iterationdeferred and defect correctionsdiscrete Newton methods

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Numerical methods for integral equations (65R20) Extrapolation to the limit, deferred corrections (65B05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items

B-convergence properties of defect correction methods. I, II, Adjoint and defect error bounding and correction for functional estimates, Asymptotic error expansions for defect correction iterates, Asymptotic expansion for the discretization error in linear elliptic boundary value problems on general regions, Commutativity of differentiation and discretization with special reference to finite element and finite difference discretizations, Gaussian collocation via defect correction, Grid strategy and high accuracy via defect corrections for the Kreiss- method for stiff boundary value problems, Iterated defect correction of differential equations. II: Numerical experiments

Cites Work

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• Local spline approximation methods
• On the estimation of errors propagated in the numerical integration of ordinary differential equations
• The method of iterated defect-correction and its application to two-point boundary value problems. I
• The defect correction principle and discretization methods
• Iterated defect correction for differential equations. I: Theoretical results
• Spline approximation by quasiinterpolants
• Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode
• Asymptotic expansions for the error of discretization algorithms for non- linear functional equations
• On improving an approximate solution of a functional equation by deferred corrections
• Iterated deferred corrections for nonlinear operator equations
• A Theoretical Framework for Proving Accuracy Results for Deferred Corrections
• Asymptotic Expansions for Product Integration
• Numerov’s Method with Deferred Corrections for Two-Point Boundary-Value Problems
• On Extrapolation Algorithms for Ordinary Initial Value Problems
• On Discretization and Differentiation of Operators with Application to Newton’s Method
• Über die Lösung der im Banachschen Raume definierten nichtlinearen Gleichungen