University of Manchester Developing a Delay Diierential Equation Solver Department of Mathematics Developing a Delay Diierential Equation Solver

University of Manchester Stability Boundaries Revisited -runge-kutta Methods for Delay Diierential Equations Department of Mathematics

Parallel Diierential-algebraic Equation Solvers for Power System Transient Stability Analysis

Real-time or faster-than-real-time power system transient stability simulations will have signiicant impact on the future design and operations of both individual electrical utility companies and large interconnected power systems. The analysis involves solution of extremely large systems of diierential and algebraic equations. Diierential-Algebraic Equation (DAE) solvers have been used to solv...

Pitfalls in Parameter Estimation for Delay Diierential Equations Department of Mathematics Pitfalls in Parameter Estimation for Delay Diierential Equations

In honour of Bill Gear on the celebration of his sixtieth birthday. Abstract Given a set of data fU(i) u(i ; p ?)g corresponding to the delay diierential equation u 0 (t; p) = f(t; u(t; p); u((t; p); p); p) for t t 0 (p); u(t; p) = (t; p) for t t 0 (p); the basic problem addressed here is that of calculating the vector p ? 2 R n. (We also consider neutral diierential equations.) Most approaches...

University of Manchester Explicit Runge-kutta Methods for the Numerical Solution of Singular Delay Diierential Equations Department of Mathematics Explicit Runge-kutta Methods for the Numerical Solution of Singular Delay Diierential Equations

In this paper we are concerned with the development of an explicit Runge-Kutta scheme for the numerical solution of delay diierential equations (DDEs) where one or more delay lies in the current Runge-Kutta interval. The scheme presented is also applicable to the numerical solution of Volterra functional equations (VFEs), although the theory is not covered in this paper. We also derive the stab...

University of Cambridge on Neutral Functional-diierential Equations with Variable Time Delays on Neutral Functional-diierential Equations with Variable Time Delays

This paper deals with an initial value problem of a neutral functional diierential equation with variable time delay. The eeect of the neutral term on the existence and uniqueness of solutions is investigated. A comparison theorem is given and is applied to the Shabat equation. The asymptotic behaviour of solutions of a linear perturbation of the generalised pantograph equation is studied.