Third‐order methods for first‐order hyperbolic partial differential equations

Abstract

SUMMARYIn this paper numerical methods for solving ÿrst-order hyperbolic partial di erential equations are developed. These methods are developed by approximating the ÿrst-order spatial derivative by third-order ÿnite-di erence approximations and a matrix exponential function by a third-order rational approximation having distinct real poles. Then parallel algorithms are developed and tested on a sequential computer for an advection equation with constant coe cient and a non-linear problem.

Chaotic oscillations of linear hyperbolic PDE with variable coefficients and implicit boundary conditions

“…This is partly because the rigorous proof of the existence of their chaotic behaviors is challenging. For more results on the chaos in infinite-dimensional dynamical systems, we refer to [7,15,21,22,23,24] and the references therein.…”