Collections > UNC Chapel Hill Undergraduate Honors Theses Collection > Numerical Confirmation of High-Frequency Defects in Discrete Waves

Abstract. We study the discrepancies between the continuous versus discretized wave equations. Motivated by the theoretical study of so-called "spurious" high-frequency wave packets initiated in [1], we use the finite difference algorithm to approximate solutions to a one-dimensional wave equation on S1 at low and high frequencies. We numerically compare these approximate solutions to the explicit continuous solutions using the discrete analog of the usual wave energy. For low frequencies there is good agreement, while for high frequencies there is very bad agreement. We explain this high frequency phenomenon heuristically by observing that, for initial data resulting in propagation in one direction only, the approximate solution nevertheless has non-trivial wave packets propagating in both directions.