Numerical Solution of Sturm-Liouville ProblemsNumerical methods date from the 1920s: in quantum physics literature, often for one type of problem and of limited accuracy; in numerical literature, accurate and efficient on a class of (usually regular) problem but hard to automate. General ODE boundary value software solves SLPs reliablybut inefficiently. It is worth developing special methods to cope with the variety of behaviour singular SLPs display. The book is intended for the scientist/engineer who wants simple methods for simple SLPs but needs to know their limitations, the algorithms that overcome these and the software that embodies these algorithms. It is also for the numerical analyst who wants a reference on good SLP methods, theirtheory, implementation and performance. The basic mathematical theory as it relates to algorithms is covered in some detail. There are numerous problems. |
Contents
Introductory background | 1 |
Elementary theory of the classical | 19 |
6 | 40 |
Copyright | |
13 other sections not shown
Common terms and phrases
accuracy admissible functions algorithm approximation asymptotic barrier BC functions behaviour Bessel Bessel equation bound boundary conditions Chapter coefficient functions Coffey-Evans computed continuous spectrum convergence corresponding defined derivatives differential equation eigenfunction EqLNF example exponentially extrapolation formula Friedrichs BC given gives Green's identity ill-conditioned initial value integration interval limit-circle limit-point linear Liouville Liouville normal form LPN/O Marletta matching point Mathieu Mathieu equation mesh meshpoints miss-distance nonoscillatory Number of eigenvalues Numerov's method oscillator oscillatory parameter perturbation Problems Problem Pruess method Prüfer equations regular BC regular problem resonance Richardson extrapolation satisfying scalar Schrödinger equation Section self-adjoint shooting method shows simple singular endpoints singular problems SLDE SLEDGE SLEIGN solution solver solving square-integrable stepsize Sturm-Liouville problems subdominant symmetric Theorem theory tion transformed tridiagonal truncated variable vector Wronskian zero θλ λο λω ди