Solution of second order differential equations using the Godunov integration method

Abstract

This MS Thesis proposes the use of an integration technique due to Godunov for the direct numerical solution of systems of second order differential equations. This method is to be used instead of the conventional technique of separating each second order equation into two first order equations and then solving the resulting system with one of the many methods available for systems of first order differential equations. Stability domains and expressions for the truncation error will be developed for this method when it is used to solve the wave equation, a passive mechanical system, and a passive electrical circuit. It will be shown both analytically and experimentally that the Godunov method compares favorably with the Adams-Bashforth third order method when used to solve both the wave equation and the mechanical system, but that there are potential problems when this method is used to simulate electrical circuits which result in integro-differential equations.