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(1978)
ACM Transactions on MathemaUcal Software
P. Bailey (1966)
Sturm-Liouville Eigenvalues via a Phase FunctionSiam Journal on Applied Mathematics, 14
Attenuation of Raylelgh-Taylor mstabdltles in a Gaussian stratification Private C6mmumcatlon
G. Adam, L. Ixaru, A. Corciovei (1976)
A first-order perturbative numerical method for the solution of the radial schrödinger equationJournal of Computational Physics, 22
B.A Hargrave (1976)
Numerical approximation of eigenvalues of Sturm-Liouville systemsJournal of Computational Physics, 20
L. Shampine, H. Watts (1976)
Global Error Estimates for Ordinary Differential EquationsACM Trans. Math. Softw., 2
C. Coll, C. Melius (1976)
Theoretical calculation of Raman scattering cross sections for use in flame analysis
(1962)
Ezgenfunctton Expansmns, Part I
Automatic Solution of the Sturm-Liouville Problem P B. BAILEY, M. K. GORDON, and L. F SHAMPINE Sand)a Laborator)es A general purpose algorithm is described for the automatic computation of eigenvalues and eigenfunctions of Sturm-Llouvllle problems, both singular and nonsmgular The method is based on the solution of initial value problems, using an integrator with a built-in global error estimating capabihty Problems arising in the construction of a satisfactory algorithm for this task are described, as are some of the software engineering aspects The resulting algorithm has performed satisfactorily on a sizable list of test problems Key Words and Phrases" elgenvalues, eigenfunctions, Sturm-Liouville problem, singular boundary value problem, mathematical software CR Categories 3 1, 3 2, 5 16, 5 17 INTRODUCTION Although there have been many codes constructed for solving special types of Sturm-Liouville eigenvalue problems, both singular and nonsingular, there seem to be none which are widely applicable: singular problems seem to be treated on a case-by-case basis, as are the effects on the accuracy of the computed eigenvalue of such things as local integration tolerance or truncation of an infinite interval. No doubt any given scheme for computing eigenvalues of singular SturmLiouville problems can be made to
ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery
Published: Sep 1, 1978
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