Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable...

We discuss numerical schemes for various forms of the Landau–Lifshitz equation. A new simple projection method is introduced and is shown to be unconditionally stable. The advantages over other schemes are also demonstrated numerically.

On the basis of analyzing the relationship between the equipment system and spare parts inventory, this paper proposes two-level equipment and spare parts system management based on the Theory of Constraints. From the system point of view and according to the Theory of Constraints, the manufacturing organization identifies bottleneck equipments in equipment system and makes the bottleneck equip...

This paper examines the stability and convergence of discretisa-tions of initial value p.d.e.'s using spatial discretisation followed by time integration with an explicit one-step method. A Cauchy integral representation is used to bound the growth in the discrete solution. New results are obtained regarding suucient conditions for both algebraic and strong stability. Suucient conditions are al...

The weighted essentially non-oscillatory method (WENO) is an excellent spatial discretization for hyperbolic partial differential equations with discontinuous solutions. However, the time-step restriction associated with explicit methods may pose severe limitations on their use in applications requiring large scale computations. An efficient implicit WENO method is necessary. In this paper, we ...

Consider a second-order linear 2-point boundary value problem (BVP) −z + p(x)z + q(x)z = r(x) (10.1) z(a) = α (10.2) z(b) = β (10.3) where p(x), q(x) and r(x) are given. By defining y(x) := [z(x), z (x)] T , the problem can be changed into a first-order differential system y = 0 1 q(x) p(x) y + 0 −r(x) (10.4) y 1 (a) − α = 0 (10.5) y 2 (b) − β = 0. (10.6) Remark. In general, a linear 2-point BV...

Article history: Received 23 May 2011 Received in revised form 3 October 2011 Accepted 27 November 2011 Available online 13 December 2011

A simple method for animation of water waves is presented. The two-dimensional wave equation with damping is used to obtain a finite difference scheme for height distribution. A computational procedure employs explicit time integration. High frame rates are typically obtained for real-time animation of water waves.