Mathematical Sciences: On the Numerical Computation of the Spectrum of Singular Sturm-Liouville Problems

主要研究者研究了正则Sturm-Liouville问题对奇异自伴Sturm-Liouville问题谱的逼近。他们把精力集中在这样的猜想上，即奇异问题谱中的任何一点都是一族正则问题的特征值序列的极限，以及它的计算结果。SLEIGN是计算Sturm-Liouville问题本征值的SLEIGN代码的继承者，主要致力于SLEIGN代码的开发。Sturm-Liouville问题出现在输运理论、量子物理、量子化学、地球物理和声学中。计算它们的解是很重要的。在问题经常出现的情况下，可以使用几个软件代码来帮助计算解决方案。该项目致力于为奇异问题创建软件。

The principal investigators study the approximation of the spectrum of singular self-adjoint Sturm-Liouville problems by regular Sturm-Liouville problems. They focus efforts on the conjecture that any point in the spectrum of a singular problem is the limit of a sequence of eigenvalues of a family of regular problems, and on its computational consequences. A major part of the effort is devoted to development of SLEIGN2, a successor to the SLEIGN code for computing eigenvalues of Sturm-Liouville problems. Sturm-Liouville problems arise in transport theory, quantum physics, quantum chemistry, geophysics, and acoustics. Computation of their solutions is important. Where the problem is regular, several software codes are available to help calculate solutions. This project undertakes to create software for singular problems.