메뉴 건너뛰기




Volumn 25, Issue 1, 1999, Pages 21-57

A test package for Sturm-Liouville solvers

Author keywords

D.2.5 Software Engineering : Testing and Debugging; D.3.2 Programming Languages : Language Classifications Fortran 77; Fortran 90; G.1.7 Numerical Analysis : Ordinary Differential Equations boundary value problems

Indexed keywords


EID: 0039179991     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/305658.287651     Document Type: Article
Times cited : (29)

References (39)
  • 1
    • 0039140911 scopus 로고    scopus 로고
    • On the approximation of eigenvalues of sturm-liouville problems by those of suitably chosen regular ones
    • Knoxville, TN, D. Hinton and P. W. Schaefer, Eds. Marcel Dekker, Inc., New York, NY
    • BAILEY, P. 1997. On the approximation of eigenvalues of Sturm-Liouville problems by those of suitably chosen regular ones. In Spectral Theory and Computational Methods of SturmLiouville Problems, Proceedings of the 1996 Barratt Lectures (Knoxville, TN), D. Hinton and P. W. Schaefer, Eds. Marcel Dekker, Inc., New York, NY, 171-182.
    • (1997) Spectral Theory and Computational Methods of Sturmliouville Problems, Proceedings of the 1996 Barratt Lectures , pp. 171-182
    • Bailey, P.1
  • 2
    • 0001586521 scopus 로고
    • Computing eigenvalues of singular Sturm-Liouville problems
    • BAILEY, P. B., EVERITT, W. N., AND ZETTL, A. 1991a. Computing eigenvalues of singular Sturm-Liouville problems. Results Math. 20, 391-423.
    • (1991) Results Math. , vol.20 , pp. 391-423
    • Bailey, P.B.1    Everitt, W.N.2    Zettl, A.3
  • 3
    • 0026292097 scopus 로고
    • Eigenvalue and eigenfunction computations for Sturm-Liouville problems
    • Dec.
    • BAILEY, P. B., GARBOW, B. S., KAPER, H. G., AND ZETTL, A. 1991b. Eigenvalue and eigenfunction computations for Sturm-Liouville problems. ACM Trans. Math. Softw. 17, 4 (Dec.), 491-499.
    • (1991) ACM Trans. Math. Softw. , vol.17 , Issue.4 , pp. 491-499
    • Bailey, P.B.1    Garbow, B.S.2    Kaper, H.G.3    Zettl, A.4
  • 4
    • 0039733382 scopus 로고
    • Solving sturm-liouville eigenproblems
    • Sandia National Laboratories, Albuquerque, NM
    • BAILEY, P. B., GORDON, M. K., AND SHAMPINE, L. F. 1976. Solving Sturm-Liouville eigenproblems. Tech. Rep. SAND76-0560. Sandia National Laboratories, Albuquerque, NM.
    • (1976) Tech. Rep. SAND76-0560
    • Bailey, P.B.1    Gordon, M.K.2    Shampine, L.F.3
  • 5
    • 84976808710 scopus 로고
    • Automatic solution of the Sturm-Liouville problem
    • Sept.
    • BAILEY, P. B., GORDON, M. K., AND SHAMPINE, L. F. 1978. Automatic solution of the Sturm-Liouville problem. ACM Trans. Math. Softw. 4, 3 (Sept.), 193-208.
    • (1978) ACM Trans. Math. Softw. , vol.4 , Issue.3 , pp. 193-208
    • Bailey, P.B.1    Gordon, M.K.2    Shampine, L.F.3
  • 7
    • 0000955099 scopus 로고
    • On the Weierstrass-Mandelbrot fractal function
    • BERRY, M. V. AND LEWIS, Z. V. 1980. On the Weierstrass-Mandelbrot fractal function. Proc. Roy. Soc. London A370, 459-484.
    • (1980) Proc. Roy. Soc. London , vol.A370 , pp. 459-484
    • Berry, M.V.1    Lewis, Z.V.2
  • 8
    • 0040325165 scopus 로고
    • Theoretical calculation of raman scattering cross-sections for use in flame analysis
    • Sandia National Laboratories, Albuquerque, NM
    • COLL, C. F. AND MELIUS, M. 1976. Theoretical calculation of Raman scattering cross-sections for use in flame analysis. Tech. Rep. SAND76-8204. Sandia National Laboratories, Albuquerque, NM.
    • (1976) Tech. Rep. SAND76-8204
    • Coll, C.F.1    Melius, M.2
  • 9
    • 0020203926 scopus 로고
    • On rossby waves modified by basic shear, and barotropic instability
    • DRAZIN, P. G., BEAUMONT, D. N., AND COAKER, S. 1982. On Rossby waves modified by basic shear, and barotropic instability. J. Fluid Mech. 124, 439-456.
    • (1982) J. Fluid Mech. , vol.124 , pp. 439-456
    • Drazin, P.G.1    Beaumont, D.N.2    Coaker, S.3
  • 10
    • 33750322857 scopus 로고
    • Linear operators: Part ii: Spectral theory, self adjoint operators in hilbert space
    • Wiley-Interscience, New York, NY
    • DUNFORD, N. AND SCHWARTZ, J. T. 1963. Linear Operators: Part II: Spectral Theory, Self Adjoint Operators in Hilbert Space. Pure and Applied Mathematics. Wiley-Interscience, New York, NY.
    • (1963) Pure and Applied Mathematics
    • Dunford, N.1    Schwartz, J.T.2
  • 11
    • 0023312263 scopus 로고
    • Two FORTRAN packages for assessing initial value methods
    • Mar. 1987
    • ENRIGHT, W. H. AND PRYCE, J. D. 1987. Two FORTRAN packages for assessing initial value methods. ACM Trans. Math. Softw. 13, 1 (Mar. 1987), 1-27.
    • (1987) ACM Trans. Math. Softw. , vol.13 , Issue.1 , pp. 1-27
    • Enright, W.H.1    Pryce, J.D.2
  • 12
    • 0016443950 scopus 로고
    • Comparing numerical methods for stiff systems of ODEs
    • ENRIGHT, W. H., HULL, T. E., AND LINDBERG, B. 1975. Comparing numerical methods for stiff systems of ODEs. BIT 15, 1-48.
    • (1975) BIT , vol.15 , pp. 1-48
    • Enright, W.H.1    Hull, T.E.2    Lindberg, B.3
  • 13
    • 79960961500 scopus 로고
    • Some numerical experiments with eigenvalue problems in ordinary problems in ordinary differential equations
    • R. E. Langer, Ed. University of Wisconsin Press, Madison, WI
    • FOX, L. 1960. Some numerical experiments with eigenvalue problems in ordinary problems in ordinary differential equations. In Boundary Problems in Differential Equations, R. E. Langer, Ed. University of Wisconsin Press, Madison, WI.
    • (1960) Boundary Problems in Differential Equations
    • Fox, L.1
  • 14
    • 84971166919 scopus 로고
    • Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
    • FULTON, C. T. 1977a. Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edinburgh 77A, 293-308.
    • (1977) Proc. Roy. Soc. Edinburgh , vol.77 A , pp. 293-308
    • Fulton, C.T.1
  • 15
    • 84968492701 scopus 로고
    • Parametrizations of titchmarsh's m(λ) functions in the limit-circle case
    • FULTON, C. T. 1977b. Parametrizations of Titchmarsh's m(λ) functions in the limit-circle case. Am. Math. Soc. Transl. 29, 51-63.
    • (1977) Am. Math. Soc. Transl. , vol.29 , pp. 51-63
    • Fulton, C.T.1
  • 16
    • 0032010657 scopus 로고    scopus 로고
    • The computation of spectral density functions for singular sturm-liouville problems involving simple continuous spectra
    • Mar.
    • FULTON, C. T. AND PRUESS, S. 1998. The computation of spectral density functions for singular Sturm-Liouville problems involving simple continuous spectra. ACM Trans. Math. Softw. 24, 1 (Mar.), 107-129.
    • (1998) ACM Trans. Math. Softw. , vol.24 , Issue.1 , pp. 107-129
    • Fulton, C.T.1    Pruess, S.2
  • 17
    • 0001649889 scopus 로고
    • On the determination of a differential equation from its spectral function
    • GELFAND, I. AND LEVITAN, B. M. 1955. On the determination of a differential equation from its spectral function. Am. Math. Soc. Transl. 1, 253-304.
    • (1955) Am. Math. Soc. Transl. , vol.1 , pp. 253-304
    • Gelfand, I.1    Levitan, B.M.2
  • 20
    • 0000164605 scopus 로고
    • The eigenproblem for ordinary differential equations of the second order and Heisenberg's theory of s matrices
    • KODAIRA, K. 1949. The eigenproblem for ordinary differential equations of the second order and Heisenberg's theory of S matrices. Am. J. Math. 71, 921-945.
    • (1949) Am. J. Math. , vol.71 , pp. 921-945
    • Kodaira, K.1
  • 22
    • 21844491517 scopus 로고
    • LCNO Sturm-Liouville problems - Computational difficulties and examples
    • Jan. 1995
    • MARLETTA, M. AND PRYCE, J. D. 1995. LCNO Sturm-Liouville problems - Computational difficulties and examples. Numer. Math. 69, 3 (Jan. 1995), 303-320.
    • (1995) Numer. Math. , vol.69 , Issue.3 , pp. 303-320
    • Marletta, M.1    Pryce, J.D.2
  • 23
    • 12144268141 scopus 로고
    • Diatomic molecules according to the wave machanics II. Vibration levels
    • MORSE, P. M. 1929. Diatomic molecules according to the wave machanics II. Vibration levels. Phys. Rev. 34, 59-61.
    • (1929) Phys. Rev. , vol.34 , pp. 59-61
    • Morse, P.M.1
  • 24
    • 0001069053 scopus 로고
    • On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems
    • PAINE, J. W., DE HOOG, F. R., AND ANDERSSEN, R. S. 1981. On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems. Computing 26, 123-139.
    • (1981) Computing , vol.26 , pp. 123-139
    • Paine, J.W.1    De Hoog, F.R.2    Anderssen, R.S.3
  • 25
    • 0011639230 scopus 로고
    • Performance of the sturm-liouville software package SLEDGE
    • Dept. of Mathematical Sciences, Colorado School of Mines, Golden, CO. Revised Dec. 1992
    • PRUESS, S., FULTON, C., AND XIE, Y. 1991. Performance of the Sturm-Liouville software package SLEDGE. Tech. Rep. MCS-91-19. Dept. of Mathematical Sciences, Colorado School of Mines, Golden, CO. Revised Dec. 1992.
    • (1991) Tech. Rep. MCS-91-19
    • Pruess, S.1    Fulton, C.2    Xie, Y.3
  • 26
    • 0003230336 scopus 로고
    • An asymptotic numerical method for a class of singular Sturm-Liouville problems
    • Oct. 1995
    • PRUESS, S., FULTON, C. T., AND XIE, Y. 1995. An asymptotic numerical method for a class of singular Sturm-Liouville problems. SIAM J. Numer. Anal. 32, 5 (Oct. 1995), 1658-1676.
    • (1995) SIAM J. Numer. Anal. , vol.32 , Issue.5 , pp. 1658-1676
    • Pruess, S.1    Fulton, C.T.2    Xie, Y.3
  • 27
    • 0039733365 scopus 로고    scopus 로고
    • The automatic classification of Sturm-Liouville problems
    • To be published
    • PRUESS, S., FULTON, C. T., AND XIE, Y. 2000. The automatic classification of Sturm-Liouville problems. J. Comput. Appl. Math. To be published. Currently available at http:// www.mines.edu/fs_home/spruess/papers/p41_99.ps; also at http://www.fit.edu/~cfulton/ sledge.
    • (2000) J. Comput. Appl. Math.
    • Pruess, S.1    Fulton, C.T.2    Xie, Y.3
  • 28
    • 0040919170 scopus 로고
    • Error control of phase-function shooting methods for sturm-liouville problems
    • PRYCE, J. D. 1986. Error control of phase-function shooting methods for Sturm-Liouville problems. IMA J. Num. Anal. 6, 103-123.
    • (1986) IMA J. Num. Anal. , vol.6 , pp. 103-123
    • Pryce, J.D.1
  • 29
    • 0008689293 scopus 로고
    • Numerical solution of sturm-liouville problems
    • Oxford University Press, Oxford, UK
    • PRYCE, J. D. 1993. Numerical Solution of Sturm-Liouville Problems. Monographs on Numerical Analysis. Oxford University Press, Oxford, UK.
    • (1993) Monographs on Numerical Analysis
    • Pryce, J.D.1
  • 30
    • 0040919185 scopus 로고    scopus 로고
    • SLDRIVER, a program for experimenting with Sturm-Liouville problems: User guide and installation guide
    • PRYCE, J. D. 1996. SLDRIVER, a program for experimenting with Sturm-Liouville problems: User guide and installation guide. Tech. Rep. RMCS/SEAS/JDP03/96.
    • (1996) Tech. Rep. RMCS/SEAS/JDP03/96
    • Pryce, J.D.1
  • 32
    • 0040364595 scopus 로고    scopus 로고
    • Algorithm 789: SLTSTPAK: A test package for Sturm-Liouville solvers
    • (Mar.). This issue
    • PRYCE, J. D. 1999. Algorithm 789: SLTSTPAK: A test package for Sturm-Liouville solvers. ACM Trans. Math. Softw. 25, 1 (Mar.). This issue.
    • (1999) ACM Trans. Math. Softw. , vol.25 , Issue.1
    • Pryce, J.D.1
  • 33
    • 0040919186 scopus 로고
    • Invariant imbedding and the calculation of eigenvalues for Sturm-Liouville systems
    • Sandia National Laboratories, Albuquerque, NM.
    • SCOTT, M. R., SHAMPINE, L. F., AND WING, G. M. 1969. Invariant imbedding and the calculation of eigenvalues for Sturm-Liouville systems. Tech. Rep. SC-R-69-1188. Sandia National Laboratories, Albuquerque, NM.
    • (1969) Tech. Rep. SC-R-69-1188
    • Scott, M.R.1    Shampine, L.F.2    Wing, G.M.3
  • 34
    • 0039140819 scopus 로고
    • Power-series solutions for energy eigenvalues
    • SECREST, D., CASHION, K., AND HIRSCHFELDER, J. O. 1962. Power-series solutions for energy eigenvalues. J. Chem. Phys. 37, 830-835.
    • (1962) J. Chem. Phys. , vol.37 , pp. 830-835
    • Secrest, D.1    Cashion, K.2    Hirschfelder, J.O.3
  • 37
    • 0000348458 scopus 로고
    • Numerical methods for solving radial schrödinger equations
    • Dec.
    • VANDEN BERGHE, G., FACK, V., AND DE MEYER, H. E. 1989. Numerical methods for solving radial Schrödinger equations. J. Comput. Appl. Math. 28 (Dec.), 391-401.
    • (1989) J. Comput. Appl. Math. , vol.28 , pp. 391-401
    • Vanden Berghe, G.1    Fack, V.2    De Meyer, H.E.3
  • 38
    • 34250688684 scopus 로고
    • Über gewöhnliche differentialgleichungen mit singularitäten und die zugehörigen entwicklungen willkürlicher funktionen
    • WEYL, H. 1910. Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. Math. Ann. 68, 220-269.
    • (1910) Math. Ann. , vol.68 , pp. 220-269
    • Weyl, H.1
  • 39
    • 0005115348 scopus 로고
    • Comparison of three numerical techniques for calculating eigenvalues of an unsymmetrical double minimum oscillator
    • WICKE, B. G. AND HARRIS, D. O. 1976. Comparison of three numerical techniques for calculating eigenvalues of an unsymmetrical double minimum oscillator. J. Chem. Phys. 64, 5236-5242.
    • (1976) J. Chem. Phys. , vol.64 , pp. 5236-5242
    • Wicke, B.G.1    Harris, D.O.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.