A review of pseudospectral methods for solving partial differential equations Chapter

Overview

; 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.;