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General linear method: a survey
Applied Numerical Mathematics, 1985Of the various methods devised as generalizations of the classical method of Euler, two extreme approaches are typically followed. One is to generalize the Euler method through the use of multistep methods; the other is to increase the complexity of one-step methods as in the Runge- Kutta method.
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Second derivative general linear methods
Numerical Algorithms, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Okuonghae, R. I., Ikhile, M. N. O.
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Trajectories generation under constraints by linearization method
Computer Methods in Applied Mechanics and Engineering, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rouff, Marc, Verdier, Matthieu
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The Construction of Practical General Linear Methods
BIT Numerical Mathematics, 2003The purpose of the material is to give a framework for the derivation of diagonally implicit general linear methods possesing the property of ``inherent Runge-Kutta stability'' (IRKS). These methods are chosen in such a way that the stage order \(q\) and the order \(p\) are equal and the information passed from step to step takes the form of a ...
Wright, William Matthew. +1 more
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Non-Parametric Methods in General Linear Models.
Journal of the Royal Statistical Society. Series A (General), 1986Distribution theory of rank statistics: Distribution Theory of Linear Rank-Order Statistics Distribution Theory of Signed Rank Order Statistics Distribution Theory of Multivariate Linear Rank-Order Statistics Nonparametric inference in linear models: Distribution-Free Rank-Order Tests for Some Linear Hypotheses Rank-Order Estimation Theory in Some ...
A. N. Pettitt, M. L. Puri, P. K. Sen
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Nonlinear Stability of General Linear Methods
Numerische Mathematik, 2006This paper extends the results of the important paper by \textit{J. C. Butcher} [The equivalence of algebraic stability and \(AN\)-stability, BIT 27, 510--533 (1987; Zbl 0637.65083)], and by \textit{G. Dahlquist} [\(G\)-stability is equivalent to \(A\)-stability, BIT 18, 384--401 (1978; Zbl 0413.65057)].
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General linear methods for y′′ = f (y (t))
Numerical Algorithms, 2012In this paper we consider the family of General Linear Methods (GLMs) for the numerical solution of special second order Ordinary Differential Equations (ODEs) of the type y???=?f(y(t)), with the aim to provide a unifying approach for the analysis of the properties of consistency, zero-stability and convergence.
D'AMBROSIO, RAFFAELE +2 more
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Strong Stability Preserving Integrating Factor General Linear Methods
Computational and Applied Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pari Khakzad +4 more
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Multistep Methods and General Linear Methods
1987This chapter is devoted to the study of multistep and general multivalue methods. After retracing their historical developement (Adams, Nystrom, Milne, BDF) we study in the subsequent sections the order, stability and convergence properties of these methods.
Ernst Hairer +2 more
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Linear and non-linear stability for general linear methods
BIT, 1987Stability in a numerical method prevents the growth of the approximate solution of a differential equation for which the solution is bounded. A variety of concepts of stability have been developed. For one-leg methods, two extremes, namely A-stability and algebraic stability together with a spectrum between these extremes are equivalent.
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