Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Surveying the state of higher education in energy efficiency, in Australian engineering curriculum

This paper presents the method and results of a survey of 27 of the 33 Australian universities teaching engineering education in late 2007, undertaken by The Natural Edge Project (hosted by Griffith University and the Australian National University) and supported by the National Framework for Energy Efficiency. This survey aimed to ascertain the extent of energy efficiency (EE) education, and to identify preferred methods to assist in increasing the extent to which EE education is embedded in engineering curriculum. In this paper the context for the survey is supported by a summary of the key results from a variety of surveys undertaken over the last decade internationally. The paper concludes that EE education across universities and engineering disciplines in Australia is currently highly variable and ad hoc. Based on the results of the survey, this paper highlights a number of preferred options to support educators to embed sustainability within engineering programs, and future opportunities for monitoring EE, within the context of engineering education for sustainable development (EESD).