Home > Publications > The Predicted Sequential Regularization Method for Differential-Algebraic Equations

The Predicted Sequential Regularization Method for Differential-Algebraic Equations

Abstract:

Differential-algebraic equations (DAEs) can be used to describe the evolution of many interesting and important systems.

This report will involve the investigation of numerical methods for solving DAEs. In particular, a new numerical method called the Predicted Sequential Regularization Method (PSRM) will be examined.

It will be shown that the concept of the index of a DAE leads to a simple and intuitive method for the solution of DAEs that unfortunately does not work particularly well. Through a simple example, the benefits of the PSRM over this intuitive method will be demonstrated. The implementation of the PSRM will be discussed including the ideas of embedded Runge-Kutta and continuous Runge-Kutta.

Author: Colin B. Macdonald

Advisor: Raymond J. Spiteri

Download: math2423_project_cmacdonald_2000