Other Schemes

Difference scheme (3.18) is but the simplest form of approximation to (3.1), and, though it is indeed extremely useful, it does suffer from frequency warping error, i.e., the sinusoid generated by scheme (3.18) under stability condition (3.25). Related to this warping effect is the fact that for high values of $\omega _{0}$, the sampling rate may have to be chosen quite high in order to satisfy (3.25) itself. In this section, various techniques for the construction of improved finite difference schemes are presented