An Efficient Method of Computing Eigenvalues in Heat Conduction

Efficient algorithms for computing eigenvalues for heat conduction problems in Cartesian and spherical coordinates are given. Explicit approximate relations are presented that generally provide accurate results. When these approximate relations are followed by a high-order Newton root-finding iteration, a high degree of accuracy can be realized. It is demonstrated that in Cartesian coordinates, eigenvalues with excellent accuracy are obtained over the entire range of parameters.