Order stars and rational approximants to exp(z)

DOI10.1016/0168-9274(89)90024-XzbMath0674.65043OpenAlexW2096550366MaRDI QIDQ1121651

Arieh Iserles, Syvert P. Nørsett

Publication date: 1989

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(89)90024-x

zbMATH Keywords

Padé approximationfittingmatrix exponentialorder starA-acceptable scheme

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Padé approximation (41A21) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (9)

Stability of Runge--Kutta methods in the numerical solution of equation \(u'(t)=au(t)+a_{0}u([t)\).] ⋮ Stability analysis of Runge–Kutta methods for differential equations with piecewise continuous arguments of mixed type ⋮ Stability of Runge-Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments ⋮ The numerical asymptotically stability of a linear differential equation with piecewise constant arguments of mixed type ⋮ Stability analysis of Runge-Kutta methods for systems \(u'(t)=Lu(t)+Mu([t)\)] ⋮ Stability of Runge-Kutta methods in the numerical solution of equation \(u'(t)=au(t)+a_{0} u([t)+a_{1} u([t-1])\)] ⋮ A 17th-order radau IIA method for package \texttt{RADAU}. Applications in mechanical systems ⋮ Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments ⋮ Stability of Runge-Kutta methods in the numerical solution of linear impulsive differential equations

Cites Work

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• Stability and accuracy of difference schemes for hyperbolic problems
• On the A-acceptability of Padé-type approximants to the exponential with a single pole
• Stability of explicit time discretizations for solving initial value problems
• Stability and accuracy of time discretizations for initial value problems
• C-polynomials for rational approximation to the exponential function
• Unconditionally stable methods for second order differential equations
• The real-pole sandwich for rational approximations and oscillation equations
• G-stability is equivalent toA-stability
• Stability and Accuracy of Semi-discretized Finite Difference Methods
• Frequency Fitting of Rational Approximations to the Exponential Function
• The Optimal Accuracy of Difference Schemes
• Order Stars, Approximations and Finite Differences I. The General Theory of Order Stars
• Order Stars, Approximations and Finite Differences II. Theorems in Approximation Theory
• Order Stars, Approximations and Finite Differences. III Finite Differences for $u_t = \omega u_{xx} $
• Accuracy Bounds for Semidiscretizations of Hyperbolic Problems
• Rational Approximations to the Exponential Function with Two Complex Conjugate Interpolation Points
• Order stars and stability theorems
• On the A-Acceptability of Rational Approximations that Interpolate the Exponential Function
• Rational Interpolation to $\exp ( - x)$ with Application to Certain Stiff Systems
• Order Stars and a Saturation Theorem for First-order Hyperbolics
• Two-Parameter, Arbitrary Order, Exponential Approximations for Stiff Equations

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