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- J. C. Butcher
- 2008

Contents Preface to the first edition xiii Preface to the second edition xvii 1 Differential and Difference Equations 1 10 Differential Equation Problems 1 100 Introduction to differential equations 1 101 The Kepler problem 4 102 A problem arising from the method of lines 7 103 The simple pendulum 10 104 A chemical kinetics problem 14 105 The Van der Pol… (More)

- R J Irwin, M J Hautus, J C Butcher
- Perception & psychophysics
- 1999

If observers in a same-different experiment base their decisions on the absolute difference between observations on a trial, the area under the receiver operating characteristic equals the maximum proportion of correct decisions that an unbiased independent-observations observer could attain. Even though the differencing strategy is suboptimal, the area… (More)

- C T H Baker, J C Butcher, C A H Paul
- 1992

STRIDE is intended as a robust adaptive code for solving initial value problems for ordinary diierential equations (ODEs). The acronym STRIDE stands for STable Runge-Kutta Integrator for Diierential Equations. Our purpose here is to report on its adaptation for the numerical solution of a test set of delay and neutral diierential equations 6].

Review In seven short sections the author reviews the notion of stiffness, Dahlquist's definition and motivation for considering A-stable numerical methods, subsequent generalized stability concepts, classical barrier results, and proofs using more recent tools such as order stars and order arrows. The paper can be recommended as a very direct entry to the… (More)

- J. C. BUTCHER
- 2010

Let a = (1 + sj §)/2 and consider the set of sequences where a sequenceU = (UQ, U%, 112, •-) is in S iff it satisfies the conditions (1) uo, u\, U2, — are positive integers (2) u satisfies the Fibonacci difference e q u a t i o n ^ = Un-l +u n-2 (n = 2,3,4,—) (3) there does not exist an integer* such that \ax-ui\ < Yz (4) \aut-U2\ < 34. Note that, for given… (More)

- J. C. Butcher
- Numerical Algorithms
- 2015

General linear methods are multistage multivalue methods. This large family of numerical methods for ordinary differential equations, includes Runge–Kutta and linear multistep methods as special cases. G-symplectic general linear methods are multivalue methods which preserve a generalization of quadratic invariants. If Q is an invariant quadratic form then… (More)

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