... Fehlerabschätzungen bei Differenzenmethoden zur numerischen Integration gewöhnlicher Differentialgleichungen Germund Dahlquist, Germund Dahlquist StockholmSearch for more papers by this author Germund Dahlquist, Germund Dahlquist StockholmSearch for more papers by this author First ...
Tópico(s): Engineering and Materials Science Studies
1951 - Wiley | ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
... 0705056PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Germund Dahlquist, Convergence and stability in the numerical integration of ... 33–53 MR0080998 0071.11803 CrossrefGoogle Scholar[2] Germund Dahlquist, Stability and error bounds in the numerical integration ...
Tópico(s): Differential Equations and Numerical Methods
1968 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
... PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Germund Dahlquist, Convergence and stability in the numerical integration of ... 33–53 MR0080998 0071.11803 CrossrefGoogle Scholar[2] Germund Dahlquist, Stability and error bounds in the numerical integration ...
Tópico(s): Advanced Numerical Methods in Computational Mathematics
1961 - Society for Industrial and Applied Mathematics | Journal of the Society for Industrial and Applied Mathematics
... to a seminal paper by the Swedish mathematician Germund Dahlquist, this review paper starts by discussing the celebrated ...
Tópico(s): Power System Optimization and Stability
2022 - Elsevier BV | Journal of Computational Physics
Some important early contributions of Germund Dahlquist are reviewed and their impact to recent developments in the numerical solution of ordinary differential equations is shown. This work is ...
Tópico(s): Electromagnetic Simulation and Numerical Methods
2006 - Springer Science+Business Media | BIT Numerical Mathematics
In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive ...
Tópico(s): Stability and Control of Uncertain Systems
2006 - Springer Science+Business Media | BIT Numerical Mathematics
Roger Barnard, Germund Dahlquist, Kent Pearce, Lothar Reichel, Kendall C. Richards,
Let {φk}nk=0,n<m, be a family of polynomials orthogonal with respect to the positive semi-definite bilinear form(g, h)d:=1m∑j=1mg(xj)h(xj),xj:=−1+(2j−1)/m.These polynomials are known as Gram polynomials. The present paper investigates the growth of |φk(x)| as a function ofkandmfor fixedx∈[−1, 1]. We show that whenn⩽2.5m1/2, the polynomials in the family {φk}nk=0are of modest size on [−1, 1], and they are therefore well suited for the approximation of functions on this interval. We also demonstrate that ...
Tópico(s): Fractional Differential Equations Solutions
1998 - Elsevier BV | Journal of Approximation Theory
Three methods, old but not so well known, transform an infinite series into a complex integral over an infinite interval. Gauss quadrature rules are designed for each of them. Various questions concerning their construction and application are studied, theoretically or experimentally. They are so efficient that they should be considered for the development of software for special functions. Applications are made to slowly convergent alternating and positive series, to Fourier series, to the numerical ...
Tópico(s): Fractional Differential Equations Solutions
1997 - Springer Science+Business Media | BIT Numerical Mathematics
An algorithm for accurate numerical inversion of slowly convergent Fourier and Laplace Transforms is studied. It makes use of several equidistant grids with the same number of points, covering different symmetric intervals of the time and frequency axes. Typically, the number of operations per computed function value is about twice as large as for an ordinary FFT. The distribution of points is, however, for many applications much more adequate because, globally, the union of the grids is an approximately ...
Tópico(s): Image and Signal Denoising Methods
1993 - Springer Science+Business Media | BIT Numerical Mathematics
Tópico(s): Matrix Theory and Algorithms
1985 - Springer Science+Business Media | BIT Numerical Mathematics
... to a seminal paper by the Swedish mathematician Germund Dahlquist, this review paper starts by discussing the celebrated ...
Tópico(s): Electromagnetic Simulation and Numerical Methods
1984 - Elsevier BV | Computer Methods in Applied Mechanics and Engineering
Germund Dahlquist, Werner Liniger, Olavi Nevanlinna,
Two of the most commonly used methods, the trapezoidal rule and the two-step backward differentiation method, both have drawbacks when applied to difficult stiff problems. The trapezoidal rule does not sufficiently damp the stiff components and the backward differentiation method is unstable for certain stable variable-coefficient problems with variable-steps. In this paper we show that there exists a one-parameter family of two-step, second-order one-leg methods which are stable for any dissipative ...
Tópico(s): Computational Fluid Dynamics and Aerodynamics
1983 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
The properties and possibilities of one-leg methods are presented in a manner that admits the generalization to smoothly varying step size. A new definition is given of the local truncation error and of the order of consistency. Some data are given for the most accurate one-leg methods, i.e. for $p = k$ and $p = k + 1$, where p is the order of consistency and k is the step number of the method.
Tópico(s): Advanced Numerical Methods in Computational Mathematics
1983 - Society for Industrial and Applied Mathematics | SIAM Journal on Numerical Analysis
Germund Dahlquist, Huang Ming-you, Randall J. LeVeque,
Tópico(s): Electromagnetic Simulation and Numerical Methods
1983 - Springer Science+Business Media | Numerische Mathematik
Some tools of linear algebra are collected and developed for potential use in the analysis of stiff differential equations. Bounds for the triangular factors of a large matrix are given in terms of the triangular factors of an associated "minorant" matrix of lower order. Minorants are also used to produce estimates of solutions of systems of ordinary differential equations, which may be sharper than those obtained by the use of logarithmic norms.
Tópico(s): Electromagnetic Simulation and Numerical Methods
1983 - Elsevier BV | Linear Algebra and its Applications
Germund Dahlquist, Lennart Edsberg, Gunilla Sköllermo, Gustaf Söderlind,
Tópico(s): Spectroscopy and Quantum Chemical Studies
1982 - Springer Nature | Lecture notes in mathematics
Petter E. Bjørstad, Germund Dahlquist, Eric H. Grosse,
A modified Aitken formula permits iterated extrapolations to efficiently estimates 221E; froms n when an asymptotic expansion $$\int_0^x {(T_k^* (t)/(x^p - t^p )^\alpha ) } dt, 0 \mathbin{\lower.3ex\hbox{$\buildrel<\over{\smash{\scriptstyle=}\vphantom{_x}}$}} x \mathbin{\lower.3ex\hbox{$\buildrel<\over{\smash{\scriptstyle=}\vphantom{_x}}$}} 1,$$ holds for some (unknown) coefficientsc j . We study the truncation and irregular error and compare the method with other forms of extrapolation.
Tópico(s): Particle physics theoretical and experimental studies
1981 - Springer Science+Business Media | BIT Numerical Mathematics
In 1975 the author showed that a norm (Liapunov function) can be constructed for the stability and error analysis of a linear multistep method (and the related one-leg method) for the solution of stiff non-linear systems, provided that the system satisfies a monotonicity condition and the method possesses a property calledG-stability. In this paper it is shown thatG-stability is equivalent toA-stability. More generally, a Liapunov function exists if the stability region of the method contains a circle ( ...
Tópico(s): Model Reduction and Neural Networks
1978 - Springer Science+Business Media | BIT Numerical Mathematics
Tópico(s): Advanced Numerical Methods in Computational Mathematics
1978 - Springer Science+Business Media | BIT Numerical Mathematics
Tópico(s): Matrix Theory and Algorithms
1976 - Springer Nature | Lecture notes in mathematics
Germund Dahlquist, Stanley C. Eisenstat, Gene H. Golub,
Tópico(s): Advanced Optimization Algorithms Research
1972 - Elsevier BV | Journal of Mathematical Analysis and Applications
Lydia Kronsjö, Germund Dahlquist,
By “Richardson extrapolation from 2h andh toh/2” the results of computations with coarse grids are used for the construction of an initial approximation on finer grid. After a rather small number of iterations high accuracy is obtained. Numerical results are given for the two-dimensional Laplace equation.
Tópico(s): Numerical methods for differential equations
1972 - Springer Science+Business Media | BIT Numerical Mathematics
... 74 10.1007/BF01448839 MR1512478 CrossrefGoogle Scholar[11] Germund Dahlquist, Convergence and stability for a hyperbolic difference equation ...
Tópico(s): Advanced Mathematical Modeling in Engineering
1969 - Society for Industrial and Applied Mathematics | SIAM Review
... 1966ix+181 MR0204157 0142.16602 CrossrefGoogle Scholar[30] Germund Dahlquist, , Sven-A˙ke Gustafson and , Károly Siklósi, Convergence ...
Tópico(s): Matrix Theory and Algorithms
1968 - Society for Industrial and Applied Mathematics | SIAM Review
... 50–64 MR0159424 0123.11701 CrossrefISIGoogle Scholar[5] Germund Dahlquist, Convergence and stability in the numerical integration of ...
Tópico(s): Advanced Numerical Methods in Computational Mathematics
1967 - Society for Industrial and Applied Mathematics | SIAM Review
Germund Dahlquist, Sven-Åke Gustafson, Károly Siklósi,
Tópico(s): Advanced Optimization Algorithms Research
1965 - Springer Science+Business Media | BIT Numerical Mathematics
The trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. For this method error bounds are derived which are valid under rather general conditions. In order to make sure that the error remains bounded ast → ∞, even though the product of the Lipschitz constant and the step-size is quite large, one needs not to assume much more than that the integral curve is uniformly asymptotically stable in the sense of Liapunov.
Tópico(s): Matrix Theory and Algorithms
1963 - Springer Science+Business Media | BIT Numerical Mathematics
Tópico(s): Differential Equations and Numerical Methods
1963 - American Mathematical Society | Proceedings of symposia in applied mathematics
... 39–44 MR0094908 0087.32503 CrossrefISIGoogle Scholar[2] Germund Dahlquist, Convergence and stability in the numerical integration of ...
Tópico(s): Differential Equations and Numerical Methods
1959 - Society for Industrial and Applied Mathematics | Journal of the Society for Industrial and Applied Mathematics
Tópico(s): Numerical methods for differential equations
1956 - Aarhus University Library | MATHEMATICA SCANDINAVICA