Converting DAE models to ODE models: application to reactive Rayleigh distillation

This paper illustrates the application of an index reduction method to some differential algebraic equations (DAE) modelling the reactive Rayleigh distillation. After two deflation steps, this DAE is converted to an equivalent first-order explicit ordinary differential equation (ODE). This ODE involves a reduced number of dependent variables, and some evaluations of implicit functions defined, either from the original algebraic constraints, or from the hidden ones. Consistent initial conditions are no longer to be computed; at the opposite of some other index reduction methods, which generate a drift-off effect, the algebraic constraints remain satisfied at any time; and, finally, the computational effort to solve the ODE may be less than the one associated to the original DAE

Methods in Mathematica for Solving Ordinary Differential Equations

An overview of the solution methods for ordinary differential equations in the Mathematica function DSolve is presented.Comment: 13 page

The Differential Form Method for Finding Symmetries

This article reviews the use of differential forms and Lie derivatives to find symmetries of differential equations, as originally presented by Harrison and Estabrook, J. Math. Phys., 12 (1971), 653. An outline of the method is given, followed by examples and references to recent papers using the method.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)

Oxford, UK, 26 August 200

Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page