The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Comparison between Eysenck's and Gray's models of personality in the prediction of motivational work criteria

Impulsivity based on Gray's [Gray, J. A. (1982) The neuropsychology of anxiety: an enquiry into the function of the septo-hippocampal system. New York: Oxford University Press: (1991). The neurophysiology of temperament. In J. Strelau & A. Angleitner. Explorations in temperament: international perspectives on theory and measurement. London. Plenum Press]. physiological model of personality was hypothesised to be more predictive of goal oriented criteria within the workplace than scales derived From Eysenck's [Eysenck. H.J. (1967). The biological basis of personality. Springfield, IL: Charles C. Thompson.] physiological model of personality. Results confirmed the hypothesis and also showed that Gray's scale of Impulsivity was generally a better predictor than attributional style and interest in money. Results were interpreted as providing support for Gray's Behavioural Activation System which moderates response to reward. (C) 2001 Elsevier Science Ltd. All rights reserved.

Moderating effect of ear preference on personality in the prediction of sales performance

This study examined the relationship between ear preference, personality, and performance ratings on 203 telesales staff. Social desirability scores were a significant predictor of two relatively independent sets of supervisor ratings (actual performance and developmental potential) in interaction with ear preference. It was found that the social desirability scale was a significant positive predictor for staff preferring a right ear headset, but a negative predictor for staff preferring a left ear headset. These results were interpreted in terms of different strategies used to achieve successful sales.