ABSTRACT
Spectral methods are fundamentally different from finite difference methods for obtaining approximate numerical solutions to partial differential equations. Instead of representing the solution by a truncated Taylor’s series expansion, we expand the solution in a truncated series using some set of basis functions, or trial functions. To obtain the discrete equations to be solved numerically, we minimize the error in the differential equation, produced by using the truncated expansion, with respect to some measure. A set of test functions are used to define the minimization criterion.
