A direct method for the numerical solution of \(y=f(x,y)\)

DOI10.1007/BF02576173zbMath0573.65058OpenAlexW1994135317MaRDI QIDQ1062733

B. George

Publication date: 1984

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02576173

zbMATH Keywords

comparison of methodsnumerical exampleserror analysisdirect methodsecond orderRunge-Kutta-Nyström

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (2)

Higher order continuous solution of \(y=f(x,y,y')\) and \(y=f(x,y)\) initial value problems ⋮ Solutions of linear second order initial value problems by using Bernoulli polynomials

Cites Work

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• Klassische Runge-Kutta-Nyström-Formeln mit SchrittweitenKontrolle für Differentialgleichungen \(\ddot x= f(t,x)\)
• Über die Instabilität von Methoden zur Integration gewöhnlicher Differentialgleichungen
• A stability and error analysis of block methods for the numerical solution ofy″=f(x,y)
• A Runge‐Kutta Method for the Numerical Integration of the Differential Equation y″ = f(x, y)
• A One-Step Method for the Numerical Integration of the Differential Equation y = f(x)y + g(x)
• A class of self-starting methods for the numerical solution ofy″=f(x,y)
• The Numerical Solution of Second-Order Differential Equations not Containing the First Derivative Explicitly
• Bemerkungen zur numerischen Integration gewöhnlicher Differentialgleichungen \(n\)-ter Ordnung

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