Rational approximations for the cosine function; P-acceptability and order

DOI10.1007/BF02141924zbMath0785.65093OpenAlexW1993331427MaRDI QIDQ688109

John P. Coleman

Publication date: 14 December 1993

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02141924

zbMATH Keywords

cosine functionstability analysisrational approximationsorder of accuracy\(P\)-acceptability

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Approximation by rational functions (41A20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Computation of special functions and constants, construction of tables (65D20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (6)

\(P\)-stable Obrechkoff methods of arbitrary order for second-order differential equations ⋮ The Chebyshev methods of Panovsky and Richardson as Runge-Kutta-Nyström methods ⋮ \(P\)-stable general Nyström methods for \(y=f(y(t))\) ⋮ Mixed collocation methods for \(y=f(x,y)\) ⋮ New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously ⋮ A phase-fitted collocation-based Runge-Kutta-Nyström method

Cites Work

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• Stability of collocation-based Runge-Kutta-Nyström methods
• On the stability of rational approximations to the cosine with only imaginary poles
• An approximation theorem for second-order evolution equations
• High order P-stable formulae for the numerical integration of periodic initial value problems
• Unconditionally stable methods for second order differential equations
• Order Stars, Approximations and Finite Differences I. The General Theory of Order Stars
• Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
• Some remarks on a class of rational approximations to the cosine
• Stability of collocation methods for the numerical solution ofy″=f (x,y)
• Order stars and stability theorems
• On the A-Acceptability of Rational Approximations that Interpolate the Exponential Function
• Attainable order of rational approximations to the exponential function with only real poles
• Trigonometric Interpolation of Empirical and Analytical Functions

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