Gaussian elimination and numerical instability /

"UILU-ENG 77 1714."

Stability and convergence of variable order multistep methods,

Includes bibliographical references.

Automatic multirate methods for ordinary differential equations /

"UILU-ENG 80 1701."

Future developments in stiff integration techniques : stability of methods that do not use an exact Jacobian /

"COO-2383-0035."

Optimal stiffly stable methods for ordinary differential equations,

"COO-1469-0164."

Numerical studies of Stone's symmetric factorization and the iteration parameters, and [tau].

Thesis (M.S.)--University of Illinois.

Current United States practice for numerical analysis of dams : a report /

"February 1985."

Methods of mathematical analysis and computation.

Mode of access: Internet.

Successive approximation methods for solving optimality problems. USSR.

Translation of 2 articles from the Russian journal.

Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

Application of X-ray microtomography to numerical simulations of agglomerate breakage by distinct element method

Computer-aided tomography has been used for many years to provide significant information about the internal properties of an object, particularly in the medical fraternity. By reconstructing one-dimensional (ID) X-ray images, 2D cross-sections and 3D renders can provide a wealth of information about an object's internal structure. An extension of the methodology is reported here to enable the characterization of a model agglomerate structure. It is demonstrated that methods based on X-ray microtomography offer considerable potential in the validation and utilization of distinct element method simulations also examined.

Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.