Numerical Integration of Linear and Nonlinear Wave Equations

Authors

Laura Lynch, Florida Atlantic UniversityFollow

Date of this Version

12-2004

Document Type

Article

Comments

A Thesis presented to the Faculty of The Honors College of Florida Atlantic University In Partial Fulfillment of Requirements for the Degree of Bachelor of Arts in Liberal Arts and Sciences with a Concentration in Physics, Under the Supervision of Professor Mark Rupright
Copyright 2004 Laura Lynch

Abstract

We begin our study with an analysis of various numerical methods and boundary conditions on the well-known and well-studied advection and wave equations, in particular we look at the FTCS, Lax, Lax-Wendroff, Leapfrog, and Iterated Crank Nicholson methods with periodic, outgoing, and Dirichlet boundary conditions. We will then extend our study to the nonlinear equation g_tt = g_xx – g_t²/g, introduced by Khoklov and Novikov. The nonlinearities are similar to those seen in General Relativity, and thus our analysis establishes the effects of numerical integration and boundary condition choices on the long-term stability of gravitational wave simulations.