Moment problem formulation of the simplified ideal magnetohydrodynamics ballooning equation

A fundamentally new method for determining the eigenvalues of linear differential operators is presented. The method involves the application of moment analysis and affords a fast and precise numerical algorithm for eigenvalue computation, particularly in the intermediate and strong coupling regimes. The most remarkable feature of this approach is that it provides exponentially converging lower and upper bounds to the eigenvalues. The effectiveness of this method is demonstrated by applying it to an important magnetohydrodynamics problem recently studied by Paris, Auby, and Dagazian [J. Math. Phys. 27, 2188 (1986)]. Through the very precise lower and upper bounds obtained, this approach gives full support to their analysis