A Bibliography of Publications of Jim Hamilton Verner

Jim Hamilton Verner Queen’s University

Jeffery Hall, Room 506 Kingston, Ontario, K7L 3N6

CANADA

Tel: +1 613 545 2404 FAX: +1 613 545 2964

E-mail: jim@jhv.mast.queensu.ca (Internet)

13 October 2017 Version 1.14

Abstract

This bibliography records publications of Jim Hamilton Verner.

Title word cross-reference

5 [VZ95a].

Algebraic [Ver79b].

Butcher [Ver79b].

Certain [Ver71a]. Classification [Ver94a]. Comparison [Ver92]. Completely [SV91, SV94]. Conditions [Ver79b]. Consistent [VB68]. Continuous [VZ93, VZ94, VZ95a, VZ95b]. Contrast [Ver90]. Convergence [Ver67].

Derivation [Ver76a]. Deriving [Ver71a, Ver71b, Ver71c, Ver82, Ver94b].

Designs [GV76]. DETEST [Ver92]. Diagonal [GV76]. Difference [Ver67]. Differentiable [Ver93a]. Differential [Ver67, Ver69a, Ver69c, Ver70].

Embedded [VZ94, VZ95b]. Equation [Ver67]. Equations [Ver69a, Ver69c, Ver70]. Error [Ver78]. Estimates [Ver78]. Explicit [CV72, Ver71b, Ver71c, Ver78, Ver82, VZ93, Ver94a, VZ94, Ver94b, VS95, VZ95b, VZ95a, Ver96].

Families [Ver79a]. Finite [Ver67]. Formula [Ver90, Ver91, Ver92].

Generalizations [VB68].

High [CV72, Ver76a, Ver93a, Ver96]. High-Order [Ver76a, Ver93a, Ver96]. Hybrid [Ver71a].

Imbedded [SV91, SV94, Ver79a]. Implicit [Ver69a, Ver69b, Ver70]. Interpolants [Ver93a, VS95].

John [Ver79b].

Kutta [CV72, SV91, SV94, Ver69b, Ver71b, Ver71c, Ver76a, Ver76b, Ver78, Ver79a, Ver90, Ver91, Ver92, VZ93, Ver93a, Ver94a, VZ94, Ver94b, VZ95a, VS95, VZ95b, Ver96].

Local [Ver78]. low [Ver96].

Method [Ver76b]. Methods [CV72, VB68, Ver69a, Ver69b, Ver71a, Ver71b, Ver71c, Ver76a, Ver78, Ver79a, Ver82, VZ93, Ver93a, VZ94, VZ95b, VZ95a]. Motivation [Ver79b].

Numerical [Ver69c].

Order [CV72, Ver67, Ver69b, Ver76a, VZ93, Ver93a, VZ95a, Ver96]. Orderings [VB68]. Orders [VZ94, VZ95b, Ver93b]. Ordinary [Ver67]. Orthogonal [GV76]. Over-Relaxation [VB68].

Pairs [SV91, SV94, Ver90, Ver91, Ver92, Ver93b, Ver94a, Ver94b, VS95, Ver96].

Quadratures [Ver70].

Relaxation [VB68]. Runge [CV72, SV91, SV94, Ver69b, Ver71b, Ver71c, Ver76a, Ver76b, Ver78, Ver79a, Ver90, Ver91, Ver92, VZ93, Ver93a, Ver94a, VZ94, Ver94b, VZ95a, VS95, VZ95b, Ver96].

Scheme [Ver67, Ver94a]. Second [Ver67]. Selecting [Ver76b, Ver79b]. Simplifying [Ver79b]. singularity [Ver67]. Solution [Ver69c]. Some [CV72, Ver69b, Ver90, Ver91, Ver92]. stage [Ver96]. Strategies [Ver93b, Ver94b]. Studying [Ver94a]. Successive [VB68].

Theory [VB68, Ver79b]. Truncation

[Ver78].

using [Ver92].

Zero [GV76].

References

Cooper:1972:SER

[CV72] G. J. Cooper and J. H. Verner. Some explicit Runge–Kutta methods of high order. SIAM Journal of Numerical Analysis, 9(3):389–405, September 1972. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Geramita:1976:ODZ

[GV76] A. V. Geramita and J. H. Verner. Orthogonal designs with zero diagonal. Canadian J. Math., XXVIII(1):215– 224, 1976. CODEN CJMAAB. ISSN 0008-414X (print), 1496-4279 (electronic).

Sharp:1991:CIR

[SV91] P. W. Sharp and J. H. Verner. Completely imbedded Runge–Kutta pairs. Technical Report 1991-01, Queen’s University, Kingston, Canada, Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada., 1991. 1–24 pp. Published in [SV94].

Sharp:1994:CIR

[SV94] P. W. Sharp and J. H. Verner. Completely imbedded Runge–Kutta pairs. SIAM Journal of Numerical Analysis, 31(4):1169–1190, August 1994. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Verner:1968:GTC

[VB68] J. H. Verner and M. J. M. Bernal. On generalizations of the theory of consistent orderings for successive overrelaxation methods. Numerische Mathematik, 12:215–222, 1968. CO-DEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic).

Verner:1967:CFD

[Ver67] J. H. Verner. Convergence of a finite difference scheme for a second order ordinary differential equation with a singularity. Technical Report 001, University of London Institute of Computer Science, 1967. 19 pp.

Verner:1969:IMI

[Ver69a] J. H. Verner. Implicit methods for implicit differential equations. Lecture Notes in Mathematics, 109:261– 266, 1969. CODEN LNMAA2. ISBN 3-540-04628-3 (print), 3-540-36158-8 (e-book). ISSN 0075-8434 (print), 1617-9692 (electronic).

Verner:1969:OSI

[Ver69b] J. H. Verner. The order of some implicit Runge–Kutta methods. Numerische Mathematik, 13:14– 23, 1969. CODEN NUMMA7. ISSN 0029-599X (print), 0945-3245 (electronic).

Verner:1969:NSD

[Ver69c] James H. Verner. Numerical Solution of Differential Equations. PhD thesis, University of Edinburgh, Scotland, Department of Computer Science, University of Edinburgh, Scotland, 1969. ix + 187 + 3 appendices pp.

Verner:1970:QID

[Ver70] J. H. Verner. Quadratures for implicit differential equations. SIAM Journal of Numerical Analysis, 7(3): 373–385, September 1970. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Verner:1971:DCH

[Ver71a] J. H. Verner. On deriving certain hybrid methods. In R. S. D. Thomas and H. C. Williams, editors, Proceedings of the Manitoba Conference on Numerical Mathematics, pages 607– 626. Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada, 1971.

Verner:1971:DERa

[Ver71b] J. H. Verner. On deriving explicit Runge–Kutta methods. Technical Report 5, Queen’s University, Kingston, Canada, 1971. 1–27 pp.

Verner:1971:DERb

[Ver71c] J. H. Verner. On deriving explicit Runge–Kutta methods. In J. Ll. Morris, editor, Conference on Applications of Numerical Analysis, number 228 in Lecture Notes in Mathematics, pages 340–347. Springer-Verlag, 1971. ISBN 0-387-05656-4. Short version of the technical report [Ver71b].

Verner:1976:DHO

[Ver76a] J. H. Verner. The derivation of highorder Runge–Kutta methods. Technical Report 93, University of Auckland, New Zealand, 1976. 1–27 pp.

Verner:1976:SRK

[Ver76b] J. H. Verner. Selecting a Runge– Kutta method. In B. L. Hartnell and H. C. Williams, editors, Proceedings of the Sixth Manitoba Conference on Numerical Mathematics, pages 495– 504. Utilitas Mathematica, P.O. Box 7, University centre, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada, 1976. ISBN 0-919628-18-4.

Verner:1978:ERK

[Ver78] J. H. Verner. Explicit Runge–Kutta methods with estimates of the local truncation error. SIAM Journal of Numerical Analysis, 15(4):772–790, August 1978. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Verner:1979:FIR

[Ver79a] J. H. Verner. Families of imbedded Runge–Kutta methods. SIAM Journal of Numerical Analysis, 16 (5):857–875, October 1979. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Verner:1979:JBA

[Ver79b] J. H. Verner. John butcher’s algebraic theory: Motivation for selecting simplifying conditions. In G. H. J. van Rees and H. C. Williams, editors, Proceedings of the Ninth Manitoba Conference on Numerical Mathematics, pages 125– 155. Utilitas Mathematica, P.O. Box 7, University centre, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada, 1979. ISBN 0-919628-27-3.

Verner:1982:DEM

[Ver82] J. H. Verner. Deriving explicit methods. Text of a presentation at the Canadian Mathematics Society Seminar on Numerical Analysis, July 1982.

Verner:1990:CSR

[Ver90] J. H. Verner. A contrast of some Runge–Kutta formula pairs. SIAM Journal of Numerical Analysis, 27 (5):1332–1344, October 1990. CO-DEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Verner:1991:SRK

[Ver91] J. H. Verner. Some Runge–Kutta formula pairs. SIAM Journal of Numerical Analysis, 28(2):496–511, April 1991. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Verner:1992:CSR

[Ver92] J. H. Verner. The comparison of some Runge–Kutta formula pairs using DETEST. In S. O. Fatunla, editor, Computational Ordinary Differential Equations, Proceedings of the third and fourth Conferences on Computational Mathematics, pages 271–284. University Press PLC, Ibadan, Nigeria, S.O. Fatunla, University of Benin, Benin City, Nigeria, 1992. ISBN 978-2493-21-X.

Verner:1993:DIH

[Ver93a] J. H. Verner. Differentiable interpolants for high-order Runge–Kutta methods. SIAM Journal of Numerical Analysis, 30(5):1446–1466, October 1993. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic).

Verner:1993:SPP

[Ver93b] J. H. Verner. Strategies for pairs, I. pairs of orders 6 and 7. Technical Report 1993-09, Queen’s University, Kingston, Canada, Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada., 1993. 1–24 pp. To appear in Annals of Numerical Mathematics, Vol. 1.

Verner:1994:CSS

[Ver94a] J. H. Verner. A classification scheme for studying explicit Runge–Kutta pairs. In S. O. Fatunla, editor, Scientific Computation, Proceedings of the Fifth International Conference on Scientific Computing, Benin City, Nigeria, 1992, pages 201– 225. Ada+Jane Press, Benin City, Nigeria, S.O. Fatunla, University of Benin, Benin City, Nigeria, 1994. ISBN 978-32323-1-2.

Verner:1994:SDN

[Ver94b] J. H. Verner. Strategies for deriving new explicit Runge–Kutta pairs. Annals of Numerical Mathematics, 1(1-4):225–244, 1994. ISSN 1021-2655.

Verner:1996:HER

[Ver96] J. H. Verner. High-order explicit Runge–Kutta pairs with low stage order. Applied Numerical Mathematics: Transactions of IMACS, 22(1): 345–357, November 1996. CODEN ANMAEL. ISSN 0168-9274 (print), 1873-5460 (electronic).

Verner:1995:E45

[VS95] J. H. Verner and P. W. Sharp. Explicit Runge–Kutta 4–5 pairs with interpolants. Technical Report 1995-03, Queen’s University, Kingston, Canada, Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada., 1995. 1–20 pp.

Verner:1993:CER

[VZ93] J. H. Verner and M. Zennaro. Continuous explicit Runge–Kutta methods of order 5. Technical Report 1993-08, Queen’s University, Kingston, Canada, Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada., 1993. 1–32 pp.

Verner:1994:OEC

[VZ94] J. H. Verner and M. Zennaro. The orders of embedded continuous explicit Runge–Kutta methods. Technical Report 1994-02, Queen’s University, Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada., 1994. 1–11 pp.

Verner:1995:CER

[VZ95a] J. H. Verner and M. Zennaro. Continuous explicit Runge–Kutta methods of order 5. Mathematics of Computation, 64(211):1123–1146, July 1995. CODEN MCMPAF. ISSN 0025-5718 (paper), 1088-6842 (electronic).

Verner:1995:OEC

[VZ95b] J. H. Verner and M. Zennaro. The orders of embedded continuous explicit Runge–Kutta methods. BIT Numerical Mathematics, 35(3):

406–416, September 1995. CO-DEN BITTEL, NBITAB. ISSN 0006-3835 (print), 1572-9125 (elec-

tronic). URL http://www.mai.liu.
se/BIT/contents/bit35.html.