Asymptotic expansions for the error of discretization algorithms for non- linear functional equations

DOI10.1007/BF01397970zbMath0148.39003MaRDI QIDQ2524945

Hans J. Stetter

Publication date: 1965

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

Full work available at URL: https://eudml.org/doc/131635

zbMATH Keywords

numerical analysis

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the convergence of characteristic finite-difference methods of high accuracy for quasi-linear hyperbolic equations
• Ausdehnung des Rombergschen Prinzips
• Maximum bounds for the solutions of initial value problems for partial difference equations
• Bemerkungen zur Romberg-Integration
• Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus

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