Numerical Study of a Singular Differential Equation Relevant for the Finite β Tearing Mode in a Toroidal Plasma

The generalized Green's function method proposed by Miller and Dewar (J. Comput. Phys.66, 356 (1986)) and Pletzer and Dewar in Computational Techniques & Applications: CTAC-89, Proceedings, Int. Conf. Brisbane, 1989, edited by W. L. Hogarth and B. J. Noye, in press, for solving the singular differential equation occurring in the finite β tearing mode problem has been tested numerically on a model differential equation. This method is compatible with a variational formulation of the problem and gives accurate numerical answers with high powers of convergence with respect to the number of grid points used. When the method is extended to the more physically relevant two-sided problem at moderate pressure gradients, a less stringent condition on the Frobenius expansion is required because the principal value of the otherwise divergent integrals associated with the method is shown to exist.