Summary of Sinc numerical methods

Journal of Computational and Applied Mathematics

Volumn 121, Issue 1, 2000, Pages 379-420

  Stenger, Frank ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMAL MAPPING; FOURIER TRANSFORMS; INITIAL VALUE PROBLEMS; INTEGRAL EQUATIONS; INTEGRATION; INTERPOLATION; LAPLACE TRANSFORMS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

HILBERT TRANSFORMS; SINC NUMERICAL METHODS;

APPROXIMATION THEORY;

EID: 0034276141     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00348-4     Document Type: Article

References (66)

1. K. Al-Khaled, Theory and computation in Hyperbolic model problems, Ph.D. Thesis, University of Nebraska, 1996.
2. p Numer. Math. 44 1984 301 308
3. D.D. Ang J.R. Lund F. Stenger Complex variable and regularization methods of inversion of the Laplace transform Math. Comp. 51 1989 589 608
4. P. Anselone Collectively Compact Operator Approximation Theory and Applications to Integral Equations 1971 Prentice-Hall Englewood Cliffs, NJ
5. B. Bialecki F. Stenger Sinc-Nyström method for numerical solution of one-dimensional cauchy singular integral equations given on a smooth arc in the complex plane Math. Comp. 51 1988 133 165
6. B. Bojanov Best Quadrature Formula for a Certain Class of Analytic Functions Zastosowania Matematyki Appl. Mat. XIV 1974 441 447
7. E. Borel Sur l'interpolation C.R. Acad. Sci. Paris 124 1897 673 676
8. q(−1,1) SIAM J. Math. Anal. 16 1985 405 421
9. R. Burke, Application of the Sinc-Galerkin method to the solution of boundary value problems, M. Sc. Thesis, University of Utah, 1977.
10. P.J. Davis Errors of numerical approximation for analytic functions J. Rational Mech. Anal. 2 1953 303 313
11. D. Elliott, F. Stenger, Sinc method of solution of singular integral equations, IMACS Conference on CSIE, Philadelphia, PA, 1984, pp. 155–166.
12. W. Faltenbacher, Sinc method of solution of the Helmholtz Equation on a Half Space, University of Utah, Utah, 1984.
13. Y. Ikebe T.Y. Li F. Stenger Numerical solution of Hilbert's problem A.G. Law B. Sahney Theory of Approximation with Applications 1976 Academic Press NewYork 338 358
14. M. Jarratt J. Lund K.L. Bowers Galerkin schemes and the Sinc-Galerkin method for singular Sturm-Liouville problems J. Comput. Phys. 89 1990 41 62
15. A. Jerri The Shannon sampling theorem – its various extensions and applications: a tutorial review Proc. IEEE 65 1977 1565 1596
16. S.A. Johnson Y. Zhou M.L. Tracy M.J. Berggren F. Stenger Inverse scattering solutions by Sinc basis, multiple source moment method, – Part III: fast algorithms Ultrasonic Imaging 6 1984 103 116
17. β by Sinc functions J. Approx. Theory 66 1991 44 52
18. V.A. Kotel'nikov, On the carrying capacity of the ‘Ether’ and wire in telecommunications, Material for the First All-Union Conference on Questions of Communication, Izd. Red. Upr. Svyazi RKKA, Moscow, 1933.
19. M. Kowalski K. Sikorski F. Stenger Selected Topics in Approximation and Computation 1993 Oxford University Press Oxford
20. D.L. Lewis, A fully Galerkin method for parabolic problems, Ph.D. Thesis, Montana State University, 1989.
21. A. Lippke Analytic solution and Sinc function approximation in thermal conduction with nonlinear heat generation J. Heat Transfer (Trans. ASME) 113 1991 5 11
22. J. Lund Symmetrization of the Sinc-Galerkin method for boundary value problems Math. Comput. 47 1986 571 588
23. J. Lund K.L. Bowers Sinc Methods for Quadrature and Differential Equations 1992 SIAM Philadelphia, PA
24. 3 Math. Comput. 35 1980 747 756
25. L. Lundin F. Stenger Cardinal-type approximation of a function and its derivatives SIAM J. Numer. Anal. 10 1979 139 160
26. K. McArthur K. Bowers J. Lund Numerical implementation of the Sinc-Galerkin method for second-order hyperbolic equations Numer. Methods Partial Differential Equations 3 1987 169 185
27. J. McNamee F. Stenger E.L. Whitney Whittaker's Cardinal function in retrospect Math. Comp. 25 1971 141 154
28. P.A.P. Moran Numerical integration in the presence of singularities Acta Math. Sci. 1 1981 83 85
29. M. Mori, M. Sugihara, The double exponential transformation in numerical analysis, in: C. Wujtak (Ed.), Orthogonal Polynomials and Quadrature Formulae (Special Issue of J. Comp. Appl. Math.), to appear.
30. D. Morley, On the convergence of a Newton-like method for closed surfaces, Ph.D. Thesis, University of Utah, 1979.
31. J. Mueller, Inverse problems for singular differential equations, Ph.D. Thesis, University of Nebraska, 1997.
32. +× [0,T] , submitted for publication.
33. S. Narashimhan, K. Chen, F. Stenger, The Harmonic-Sinc solution of the Laplace equation for problems with singularities and semi-infinite domains, Numer. Heat Transfer, to appear.
34. M. O'Reilly F. Stenger Computing solutions to medical problems IEEE Trans. Automat. Control 43 1998 843 846
35. K. Parker, PTOLEMY, A Sinc collocation sub-system, Ph.D. Thesis, University of Utah, 1999.
36. K. Pfabe, A problem in nonlinear ion transport, Ph.D. Thesis, University of Newbraska, 1995.
37. G. Plana Sur une nouvelle expression analytique des nombres Bernoulliens Academia di Torino 25 1820 403 418
38. Q.I. Rahman G. Schmeisser The summation formulæ of Poisson, Plana, Euler-Maclaurin and their relationship J. Math. Sci. 28 1994 151 171
39. R. Schmidtlein, F. Stenger, A Sinc-Fortran package for conformal mapping, to appear.
40. J. Schwing, Numerical solution of integral equations in potential theory problems, Ph.D. Thesis, University of Utah, 1976.
41. p ACM TOMS 10 1984 152 160
42. C.E. Shannon, A mathematical theory of communication, Bell Systems Tech. J. 27 (1948) 379–423,623–656.
43. J. Soller, Global optimization for neural network problems, Ph.D. Thesis, University of Utah, 1994.
44. W. Squire, Numerical evaluation of integrals using Moran transformations, Aerospace Eng. Report No. Tr-14, 1969.
45. F. Stenger An analytic function which is an approximate characteristic function SIAM J. Numer. Anal. 12 1975 239 254
46. F. Stenger The approximate solution of convolution-type integral equations SIAM J. Math. Anal. 4 1973 536 555
47. F. Stenger Integration formulas based on the trapezoidal formula J. Inst. Math. Appl. 12 1973 103 114
48. F. Stenger Approximations via the Whittaker Cardinal Function J. Approx. Theory 17 1976 222 240
49. F. Stenger A Sinc-Galerkin method of solution of boundary value problems Math. Comp. 33 1979 85 109
50. F. Stenger Numerical methods based on the Whittaker Cardinal, or Sinc functions SIAM Rev. 23 1981 165 224
51. F. Stenger, Sinc methods for solving partial differential equations, in: A. Miller (Ed.), Contributions of Mathematical Analysis to the Approximate Solution of Partial Differential Equations, Proceedings of the Centre for Mathematical Analysis, Australian National University, Vol. 7, 1984, pp. 40–64.
52. F. Stenger Numerical Methods Based on Sinc and Analytic Functions 1993 Springer NewYork
53. F. Stenger Collocating convolutions Math. Comp. 64 1995 211 235
54. F. Stenger B. Barkey R. Vakili Sinc convolution method of solution of burgers’ equation K. Bowers J. Lund Proceedings of Computation and Control III 1993 Birkhäuser Basel
55. F. Stenger, S.Å. Gustafson, B. Keyes, M. O'Reilly, K. Parker, ODE-IVP-PACK, via Sinc indefinite integration and Newton iteration, Numer. Algorithms, to appear.
56. F. Stenger, A. Naghsh-Nilchi, J. Niebsch, R. Ramlau, A unified approach to the approximate solution of PDE, Comm. Appl. Anal., to appear.
57. F. Stenger, R. Schmidtlein, Conformal maps via Sinc methods, in: N. Papamichael, St. Ruscheweyh, E.B. Saff (Eds.), Computational Methods in Function Theory (CMFT ’97), World Scientific, Singapore, pp. 505–549.
58. M. Stromberg, Solution of shock problems by methods using Sinc functions, Ph.D. Thesis, University of Utah, 1988.
59. M. Sugihara, Optimality of the double exponential formula – functional analysis approach, Numer. Math. 75 (1997) 379–395 (The original paper in Japanese appeared in Kokyuroku RIMS Kyoto Univ. No. 585 (1986) 150–175).
60. H. Takahasi M. Mori Error estimation in the numerical integration of analytic functions Report Comput. Centre, Univ. Tokyo 3 1970 41 108
61. H. Takahasi M. Mori Quadrature formulas obtained by variable transformation Numer. Math. 21 1973 206 219
62. H. Takahasi M. Mori Double exponential formulas for numerical integration Publ. RIMS Kyoto Univ. 9 1974 721 741
63. E.T. Whittaker On the functions which are represented by expansion of the interpolation theory Proc. Roy. Soc. Edinburgh 35 1915 181 194
64. q(−1,1) J. Complexity 8 1992 324 335
65. K. Yee Numerical solution of boundary value problems involving Maxwell's equations in isotropic media IEEE Trans. Antennas and Propagation AP-16 1966 302 307
66. T. Zhang, F. Stenger, SINC – PACK – A Package of Sinc Algorithms, in preparation.