A review of pseudospectral methods for solving partial differential equations | CU Experts

Overview

Finite Difference (FD) methods approximate derivatives of a function bylocalarguments (such as du(x) / dx≈ (u(x+h) −u(x−h))/2h, wherehis a small grid spacing) – these methods are typically designed to be exact for polynomials of low orders. This approach is very reasonable: since the derivative is a local property of a function, it makes little sense (and is costly) to invoke many function values far away from the point of interest.