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)
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)
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)
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)
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)