Ode an Elisabeth

An Ode to Arrows

We study a number of embedded DSLs for autonomous ordinary differential equations (autonomous ODEs) in Haskell. A naive implementation based on the lazy tower of derivatives is straightforward but has serious time and space leaks due to the loss of sharing when handling cyclic and infinite data structures. In seeking a solution to fix this problem, we explore a number of DSLs ranging from shall...

An extended ode solver for sensitivity calculations

A rcccntly published semi-implicit Rung+Kulta algorithm has been extended to compute parameter sensitivities in dynamical systems. The decomposed direct method (DDM) of sensitivity analysis results in a general and compact FORTRAN program, well-suited even for small computers. The straightforward DDM provides more accurate sensitivities than does the numerically efficient, but more involved Gre...

On an ODE from forced coating ow

Stabilization of an ODE-Schrödinger cascade

We consider the problem of stabilization of a linear ODE with input dynamics governed by the linearized Schrödinger equation. The interconnection between the ODE and Schrödinger equation is bi-directional at a single point. We construct an explicit feedback law that compensates the Schrödinger dynamics at the inputs of the ODE and stabilizes the overall system. Our design is based on a two-step...

An Enhanced ODE Solver for REDUCE

Work is in progress to extend the REDUCE package ODESOLVE for solving ordinary differential equations (ODEs). The latest version has a more user-friendly and flexible interface, allows conditions to be imposed on solutions and can solve some classes of nonlinear ODEs. It performs well on recently published test examples. The interface supports systems