A programmed algorithm for existence proofs for two-point boundary value problems

DOI10.1007/BF02241862zbMath0703.65043MaRDI QIDQ916318

M. Göhlen, Johann Schroeder, Michael Plum

Publication date: 1990

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

interval arithmeticpolynomial splinesnonlinear two-point boundary value problemsexistence of a solutionNumerical resultstwo-sided error boundsEB- algorithm

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Interval and finite arithmetic (65G30) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (4)

A posteriori error bounds for two point boundary value problems: a Green's function approach ⋮ Computer-assisted existence proofs for two-point boundary value problems ⋮ Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems ⋮ Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems

Uses Software

• ACRITH-XSC
• FORTRAN-SC

Cites Work

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• Ein Axiomensystem für den Anschauungsraum. (An axiom system for the Euclidean space)
• FORTRAN-SC. A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH
• Einschließungsaussagen bei Differentialoperatoren zweiter Ordnung durch punktweise Ungleichungen
• Gleichmäßig einschließende Diskretisierungsverfahren für schwach nichtlineare Randwertaufgaben. (Uniformly enclosing discretization methods for weakly nonlinear boundary value problems)
• Monotone iteration descretization algorithm for BVP's
• Operator inequalities
• A practical guide to splines
• Schwankung von Polynomen zwischen Gitterpunkten. (Oscillations of polynomials between lattice points)
• Aufgaben monotoner Art
• A Posteriori Error Bounds for Two-Point Boundary Value Problems
• Computable a Posteriori $L_\infty $-Error Bounds for the Approximate Solution of Two-Point Boundary Value Problems

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