zbMATH — the first resource for mathematics

ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem. (English) Zbl 1198.15002
Summary: A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Eigenvalues and matrix elements computed by the ODPEVP program can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177, No. 8, 649–675 (2007; Zbl 1196.81283); ibid. 179, No. 9, 685–693 (2008; Zbl 1197.81008)]. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials, a 3D-model of a hydrogen atom in a homogeneous magnetic field and a hydrogen atom on a three-dimensional sphere.

15-04 Software, source code, etc. for problems pertaining to linear algebra
Full Text: DOI
[1] Chuluunbaatar, O.; Gusev, A.A.; Derbov, V.L.; Kaschiev, M.S.; Melnikov, L.A.; Serov, V.V.; Vinitsky, S.I., J. phys. A, 40, 11485-11524, (2007) · Zbl 1122.81327
[2] Chuluunbaatar, O.; Derbov, V.L.; Galtbayar, A.; Gusev, A.A.; Kaschiev, M.S.; Vinitsky, S.I.; Zhanlav, T., J. phys. A, 41, (2008), 295203-1-25
[3] Krassovitskiy, P.M.; Takibaev, N.Zh., Bull. Russian acad. sci. phys., 70, 815-818, (2006)
[4] Krassovitskiy, P.M.; Vinitsky, S.I.; Gusev, A.A.; Chuluunbaatar, O., Bull. Russian acad. sci. phys., 73, 233-235, (2009)
[5] Demkov, Yu.N.; Meyer, J.D., Eur. phys. J. B, 42, 361-365, (2004)
[6] Dimova, M.G.; Kaschiev, M.S.; Vinitsky, S.I., J. phys. B, 38, 2337-2352, (2005)
[7] Kazaryan, E.M.; Kostanyan, A.A.; Sarkisyan, H.A., Physica E, 28, 423-430, (2005)
[8] Chuluunbaatar, O.; Gusev, A.A.; Abrashkevich, A.G.; Amaya-Tapia, A.; Kaschiev, M.S.; Larsen, S.Y.; Vinitsky, S.I., Comput. phys. comm., 177, 649-675, (2007)
[9] Chuluunbaatar, O.; Gusev, A.A.; Vinitsky, S.I.; Abrashkevich, A.G., Comput. phys. comm., 179, 685-693, (2008)
[10] Strang, G.; Fix, G.J., An analysis of the finite element method, (1973), Prentice-Hall Englewood Cliffs, New York · Zbl 0278.65116
[11] Bathe, K.J., Finite element procedures in engineering analysis, (1982), Prentice-Hall Englewood Cliffs, New York · Zbl 0528.65053
[12] Chuluunbaatar, O.; Gusev, A.A.; Kaschiev, M.S.; Kaschieva, V.A.; Amaya-Tapia, A.; Larsen, S.Y.; Vinitsky, S.I., J. phys. B, 39, 243-269, (2006)
[13] Kuperin, Yu.A.; Kurasov, P.B.; Melnikov, Yu.B.; Merkuriev, S.P., Ann. phys., 205, 330-361, (1991)
[14] Chuluunbaatar, O.; Gusev, A.A.; Gerdt, V.P.; Rostovtsev, V.A.; Vinitsky, S.I.; Abrashkevich, A.G.; Kaschiev, M.S.; Serov, V.V., Comput. phys. comm., 178, 301-330, (2008)
[15] Abrashkevich, A.G.; Kaschiev, M.S.; Vinitsky, S.I., J. comp. phys., 163, 328-348, (2000)
[16] Vinitskii, S.I.; Mardoyan, L.G.; Pogosyan, G.S.; Sissakian, A.N.; Strizh, T.A., Phys. atom. nucl., 56, 321-327, (1993)
[17] Press, W.H.; Teukolsky, S.A.; Vetterling, W.T.; Flannery, B.P., Numerical recipes: the art of scientific computing, (1986), Cambridge University Press Cambridge · Zbl 0587.65003
[18] Abramowitz, M.; Stegun, I.A., Handbook of mathematical functions, (1965), Dover New York · Zbl 0515.33001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.