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Algorithm 621: Software with Low Storage Requirements for Two-Dimensional, Nonlinear, Parabolic Differential Equations

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Published:01 December 1984Publication History
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References

  1. 1 BRANDT, A., AND DINAR, N Multigrid solutions to elliptic flow problems. In Numerical Methods for Partial Differential Equations, S.V. Parter, Ed.Academic Press, New York, 1979 53-147.Google ScholarGoogle Scholar
  2. 2 DEW, P.M., AND WALSH, J.E. A set of library routines for solving parabolic equations in one space variable. ACM Trans. Math Softw 7, 3 (Sept. 1981), 295-314 Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3 EISENSTAT, C.S., SCHULTZ, M.H., AND SHERMAN, A.H. Application of sparse matrax methods to partial differential equations. In Proceedings of the AICA International Symposium on Computer Methods for Partial Differential Equations (Bethlehem, Pa., June 1975).Google ScholarGoogle Scholar
  4. 4 GOURLAY, A R., AND MCKEE, S. The construction of hopscotch methods for parabolic and elliptic equattons in two space dimensions with a mixed derivative. J Comput Appl. Math 3, 3 (Sept. 1977), 201-206.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5 HEMKER, P.W. Introduction to multi-grid methods. Nieuw Arch. Wiskunde 3, 29 {1981), 71- 101.Google ScholarGoogle Scholar
  6. 6 HINDMARSH, A.C. GEARB: Solution of ordinary differential equations having banded Jacobian. Rep UCID-30059, Rev. 2, Lawrence Livermore Laboratory, Livermore, Calif., June 1977.Google ScholarGoogle Scholar
  7. 7 MELGAARD, D.K., AND SINCOVEC, R.F. General software for two-dimensional nonlinear partial differential equations. ACM Trans. Math Softw 7, 1 (Mar. 1981), 106-125. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8 MELGAARD, D.K., AND SINCOVEC, R.F. Algorithm 565, PDETWO/PSETM/GEARB: Solution of systems of two-dimensional nonlinear partial dffferential equations. ACM Trans., Math Softw 7, 1 (Mar. 1981), 126-135. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9 MITCHELL, A.R., AND GRIFFITHS, D.F. The Finite Difference Method in Partial Differential Equattons. Wiley, New York, 1980Google ScholarGoogle Scholar
  10. 10 RICHTMYER, R.D, AND MORTON, K.W. Dtfference Methods for Inttial-Value Problems Interscience, New York, 1967, 201.Google ScholarGoogle Scholar
  11. 11 SHAMPINE, L.F., AND GORDON, M.K. Computer Solutwn of Ordinary Differenttal Equations Initial Value Problems W.H. Freeman, San Francisco, 1975, 118.Google ScholarGoogle Scholar
  12. 12 SPELLMANN, J W., AND HINDMARSH, A.C. GEARS" solution of ordinary differential equations having a sparse Jacobian matrix. Rep. UCID-30116, Lawrence Livermore Laboratory, Livermore, Calif, 1975Google ScholarGoogle Scholar
  13. 13 VAN DER HOUWEN, P.J., AND SOMMEIJER, B.P. A special class of multistep Runge-Kutta methods with extended real stability interval. IMA J. Numer. Anal. 2, 2 (Apr. 1982), 183-209.Google ScholarGoogle Scholar
  14. 14 VAN DER HOUWEN, P.J., AND SOMMEIJER, B.P. Analysis of Chebyshev relaxation in multigrid methods for nonlinear parabolic differential equations Z. Angew Math Mech. 63, 3 (1983), 193- 201.Google ScholarGoogle ScholarCross RefCross Ref
  15. 15 WATTS, H.A. Starting step size for an ODE solver. J Comput. Appl. Math 9, 2 (June 1983), 177-191.Google ScholarGoogle ScholarCross RefCross Ref

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  1. Algorithm 621: Software with Low Storage Requirements for Two-Dimensional, Nonlinear, Parabolic Differential Equations

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      cover image ACM Transactions on Mathematical Software
      ACM Transactions on Mathematical Software  Volume 10, Issue 4
      Dec. 1984
      120 pages
      ISSN:0098-3500
      EISSN:1557-7295
      DOI:10.1145/2701
      Issue’s Table of Contents

      Copyright © 1984 ACM

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      Publication History

      • Published: 1 December 1984
      Published in toms Volume 10, Issue 4

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