A review of pseudospectral methods for solving partial differential equations

Finite Difference (FD) methods approximate derivatives of a function by local arguments (such as d u ( x ) / d x ≈ ( u ( x + h ) − u ( x − h ))/2 h , where h is 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.