Computational Ordinary Differential Equations

This is a collection of refereed papers from an international conference which discussed initial value problems, boundary value problems, differential algebraic equations, applications to the solution of partial differential equations, parallel solution methods, and methods of conservation and global error calculation. Within each section the paper has been ordered so the reader should perceive a gradual movement from the theoretical to the practical.

Table of Contents:
Algebraic conditions for A-stable Runge-Kutta methods; Contractivity in the maximum norm for Runge-Kutta methods; Stability criteria in the numerical solution of initial value problems; Some new hybrid methods for initial value problems; A family of Nordsieck methods; Multistep methods for ordinary differential equations based on algebraic and first order trigonometric polynomials; Runge-Kutta equilibrium theory for a mixed relative/absolute error measure; Detecting stability barriers in BDF solvers; Continuous explicit Runge-Kutta methods; Dense output for the GBS extrapolation method; Methods for starting iteration schemes for implicit Runge-Kutta formulae; Efficient P-stable methods for second order systems; New continuous extensions for the Dormand and Prince RK method; The next generation of Runge-Kutta codes; Application of the Chapman-Enskog method to an asymptomatic analysis of stiff systems of ordinary differential equations; Singular perturbation phenomena for two-point boundary value problems; On the implementation of the algebraic difference scheme for stiff BVPs; Boundary value problem continuation with moving meshes; A review of some developments in collocation algorithms; Continuation and Gauss-Newton techniques; The inverse problem in ordinary differential equations; SDIRK-Methods for differential-algebraic equations of Index 1; Numerical methods for differential-algebraic equations - current status and future directions; Numerical methods for differential-algebraic equations describing constrained mechanical motion; Dynamic iteration schemes for differential in large scale circuit simulation; Towards efficient DAE solvers for the solution of dynamic simulation problems; Towards an automatic algorithm for the numerical solution of parabolic partial differential equations using the method of lines; Pragmatic experiments with Krylov methods in the stiff ODE setting; Relaxation-based integration by Runge-Kutta methods and its applications to the moving finite element method. (Part contents)