Automatic solution of Sturm-Liouville problems using the Pruess method

Abstract We develop algorithms based on coefficient approximation for the automatic solution of regular and singular Sturm–Liouville problems.

[1]  P. Hartman Ordinary Differential Equations , 1965 .

[2]  M. Eastham,et al.  Schrödinger-type operators with continuous spectra , 1982 .

[3]  S. Pruess High order approximations to Sturm-Liouville eigenvalues , 1975 .

[4]  Frank de Hoog,et al.  Uniform estimation of the eigenvalues of Sturm–Liouville problems , 1980, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[5]  L. Ixaru,et al.  Choosing step sizes for perturbative methods of solving the Schrödinger equation , 1980 .

[6]  N. A. Haskell The Dispersion of Surface Waves on Multilayered Media , 1953 .

[7]  L. Ixaru The error analysis of the algebraic method for solving the Schrödinger equation , 1972 .

[8]  H. Prüfer Neue Herleitung der Sturm-Liouvilleschen Reihenentwicklung stetiger Funktionen , 1926 .

[9]  Marco Marletta Certification of algorithm 700 numerical tests of the SLEIGN software for Sturm-Liouville problems , 1991, TOMS.

[10]  V. C. L. Hutson,et al.  Applications of Functional Analysis and Operator Theory , 1980 .

[11]  W. H. Enright,et al.  Test Results on Initial Value Methods for Non-Stiff Ordinary Differential Equations , 1976 .

[12]  John D. Pryce,et al.  Error Control of Phase-Function Shooting Methods for Sturm-Liouville Problems , 1986 .

[13]  J. Lambert Computational Methods in Ordinary Differential Equations , 1973 .

[14]  D. Arnold,et al.  Computer Solution of Ordinary Differential Equations. , 1981 .

[15]  Lawrence F. Shampine,et al.  Automatic Solution of the Sturm-Liouville Problem , 1978, TOMS.

[16]  J. Canosa,et al.  A New Method for the Solution of the Schrdinger Equation , 1970 .

[17]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[18]  Roy G. Gordon,et al.  New Method for Constructing Wavefunctions for Bound States and Scattering , 1969 .

[19]  Steven Pruess,et al.  Mathematical software for Sturm-Liouville problems , 1993, TOMS.

[20]  D. O. Banks,et al.  Computation of eigenvalues of singular Sturm-Liouville systems , 1968 .

[21]  Steven Pruess,et al.  Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation , 1973 .