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FISHPACK contains a collection of Fortran77 subroutines that solve second- and fourth-order finite difference approximations to separable elliptic Partial Differential Equations (PDEs). These include Helmholtz equations in cartesian, polar, cylindrical, and spherical coordinates, as well as more general separable elliptic equations. The solvers use the cyclic reduction algorithm. When the problem is singular, a least-squares solution is computed. Singularities induced by the coordinate system are handled, including at the origin r=0 in cylindrical coordinates, and at the poles in spherical coordinates. (Description taken from home page)
This package contains an example Simply Fortran project.