Numerical Integration of Non-Linear Wave Equations

Abstract

Solving partial differential equations is an art that can be difficult, especially when done numerically. There are many factors that must be considered. Our goal is to pick a numerical method that not only makes sense for the equation we are solving, but one that is stable over a given amount of time, one that has a sufficiently high order accuracy, and one that minimizes the time required to compute the solution while keeping the accuracy. Also, boundary conditions must be considered as they can effect a solution drastically and may cause discontinuities.