Results 141 to 150 of about 24,909,697 (184)

The existence of symplectic general linear methods

Numerical Algorithms, 2008
The paper obtains a criterion that any general linear integration method must satisfy if it is symplectic. After deriving a criterion for symplectic behavior based on a standard conservative problem of the form, \[ \begin{cases} z_1'(t)= -\alpha(z_3,z_4,\dots,z_N)z_2(t), \\ z_2'(t)= \alpha(z_3,z_4,\dots,z_N)z_1(t), \\ z_i'(t)=f_i(z_3,z_4,\dots,z_N)z_1 ...
John C. Butcher, L. L. Hewitt
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The Construction of Practical General Linear Methods

BIT Numerical Mathematics, 2003
The 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., Butcher, John C.   +1 more
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A new linearization method for generalized linear multiplicative programming

Computers & Operations Research, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chun-Feng Wang, San-Yang Liu
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Second derivative general linear methods

Numerical Algorithms, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. I. Okuonghae, M. N. O. Ikhile
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Linear convergence of generalized Weiszfeld's method

Computing, 1980
Weiszfeld's method is widely used for solving problems of optimal location. It is shown that a very general variant of this method converges linearly thus generalizing a result of I. N. Katz.
Heinrich Voß, Ulrich Eckhardt
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General linear method: a survey

Applied Numerical Mathematics, 1985
Of 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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Nonlinear Stability of General Linear Methods

Numerische Mathematik, 2006
This 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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Strong Stability Preserving General Linear Methods

Journal of Scientific Computing, 2014
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Giuseppe Izzo, Zdzislaw Jackiewicz
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Generating invariants for non-linear loops by linear algebraic methods

Formal Aspects of Computing, 2015
Abstract We present new computational methods that can automate the discovery and the strengthening of non-linear interrelationships among the variables of programs containing non-linear loops, that is, that give rise to multivariate polynomial and fractional relationships. Our methods have complexities lower than the mathematical foundations
Rachid Rebiha, Arnaldo Vieira Moura, Nadir Matringe   +2 more
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Multistep Methods and General Linear Methods

1987
This 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, Syvert Paul Nørsett, Gerhard Wanner   +2 more
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