Numerical Solution Of Sturm-liouville Problems

✍ Scribed by John Derwent Pryce

• Publisher: Oxford Univesity Press
• Year: 1993
• Tongue: English
• Leaves: 337
• Series: Monographs on Numerical Analysis
• Category: Library

✦ Synopsis

Sturm-Liouville problems (SLPs)--an applied mathematics tool developed in the nineteenth century and a driving force of pure mathematics in the early twentieth century--became of vital interest to physicists with the advent of Schrodinger's equations. Today's fascinating variety of SL-related computations reflects this diverse historical background. This book was written for scientists and engineers who desire an introduction to simple SLPs, their limitations, the algorithms that overcome these limitations, and available software. Numerical analysts seeking a reference on good SLP methods, theory, implementation, and performance will also want to own a copy of this book. Treatments of the underlying mathematical theories and numerous helpful problems round out this superb new volume.

✦ Table of Contents

Introductory background
1. Elementary theory of the classical SLP
2. Simple matrix methods
3. Variational methods
4. Shooting and the scaled Prufer method
5. Pruess methods
6. Singular SLPs: theory
7. Singular SLPs: numerical treatments
8. Computing and manipulating eigenfunctions
9. The computation of resonances
10. Further topics
11. Conclusions
A: Eigenvalues of Paine problems
B: List of test problems
C: Available Sturm-Liouville software.

✦ Subjects

Mathematics; Sturm-Liouville; Numerical Analysis; Monographs on Numerical Analysis; Differential Equations