In many problems, one wishes to solve the Helmholtz equation in cylindrical or spherical coordinates which introduces variable coefficients within the differentiated terms. Fourth order accurate methods are desirable to reduce pollution and dispersion errors and so alleviate the points-per-wavelength constraint. However, the variable coefficients renders existing fourth order finite difference ...

A~1 so obtained, however, is no longer a tridiagonal matrix. If 1 is a n X ft matrix, we will have in general n2 elements of A-1. When n is large, this method becomes unwieldy, even with an electronic computer. Linear equations similar to Eqs. (1) are frequently encountered in problems of mathematical physics. For instance, the backward finite difference method for solving the heat equation req...