Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A marching technique for nonseparable equations

Author: Louis W. Ehrlich
Journal: Math. Comp. 33 (1979), 881-890
MSC: Primary 65F10; Secondary 65N20, 68C25
MathSciNet review: 528045
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A multiple-shooting marching technique is described which is applicable to arbitrary block tridiagonal matrices derived from nonseparable difference equations which are solved many times. Comparison with other methods on a particular problem shows the method to be competitive with respect to time and storage.

References [Enhancements On Off] (What's this?)

  • [1] O. AXELSSON, On Preconditioning and Convergence Acceleration in Sparse Matrix Problems, CERN 74-10, Geneva.
  • [2] Randolph E. Bank and Donald J. Rose, Marching algorithms for elliptic boundary value problems. I. The constant coefficient case, SIAM J. Numer. Anal. 14 (1977), no. 5, 792–829. MR 0502000,
  • [3] Randolph E. Bank, Marching algorithms for elliptic boundary value problems. II. The variable coefficient case, SIAM J. Numer. Anal. 14 (1977), no. 5, 950–970. MR 0502001,
  • [4] Paul Concus, Gene H. Golub, and Dianne P. O’Leary, A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations, Sparse matrix computations (Proc. Sympos., Argonne Nat. Lab., Lemont, Ill., 1975) Academic Press, New York, 1976, pp. 309–332. MR 0501821
  • [5] L. W. EHRLICH, Iterative vs. a Direct Method for Solving Fourth Order Elliptic Difference Equations, Proc.-A. C. M. National Meeting, Los Angeles, Calif., 1966, pp. 29-35.
  • [6] Louis W. Ehrlich, The numerical solution of a Navier-Stokes problem in a stenosed tube: a danger in boundary approximations of implicit marching schemes, Comput. & Fluids 7 (1979), no. 4, 247–256. MR 568753,
  • [7] A. C. HINDMARSH, Solution of Block-Tridiagonal Systems of Linear Algebraic Equations, Lawrence Livermore Laboratory, UCID-30150, 1977.
  • [8] David S. Kershaw, The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations, J. Computational Phys. 26 (1978), no. 1, 43–65. MR 0488669
  • [9] J. A. MANTEUFFEL, An Iterative Method for Solving Nonsymmetric Linear Systems with Dynamic Estimation of Parameters, Dept. of Computer Science, Univ. of Illinois at Urbana-Champaign, UIUCDCS-R-75-758, 1975.
  • [10] J. A. Meijerink and H. A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric 𝑀-matrix, Math. Comp. 31 (1977), no. 137, 148–162. MR 0438681,
  • [10a] I. J. PEARSON & B. KAPLAN, Computer Time Comparison of Point and Block Successive Overtaxation, Report AFIT-TR-70-6, Air Force Institute of Technology, School of Engineering, Wright-Patterson AFB, Ohio, 1970.
  • [11] P. J. ROACHE, A Direct Method for the Discretized Poisson Equation, Sandia Report SC-RR-70-S79, 1971.
  • [12] P. J. ROACHE, "Marching methods for elliptic problems: Part I", Numerical Heat Transfer, v. 1, 1978, pp. 1-25.
  • [13] S. C. EISENSTAT, M. C. GURSKY, M. H. SCHULTZ & A. H. SHERMAN, Yale Sparse Matrix Package II. The Nonsymmetric Codes, Res. Report #114, Dept. of Comput. Sci., Yale Univ., 1977.
  • [14] J. F. THOMPSON, F. C. THAMES & C. W. MASTIN, "Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary twodimensional bodies," J. Computational Phys., v. 15, 1974, pp. 299-319.
  • [15] J. F. THOMPSON, F. C. THAMES & C. W. MASTIN, Boundary-Fitted Curvilinear Coordinate Systems for Solution of Partial Differential Equations on Fields Containing any Number of Arbitrary Two-Dimensional Bodies, NASA CR-2729, 1977.
  • [16] D. M. YOUNG, JR. & L. J. HAYES, Notes on the Conjugate Gradient Method, CNA Report, Univ. of Texas, Austin.
  • [17] David M. Young, Iterative solution of large linear systems, Academic Press, New York-London, 1971. MR 0305568

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F10, 65N20, 68C25

Retrieve articles in all journals with MSC: 65F10, 65N20, 68C25

Additional Information

Article copyright: © Copyright 1979 American Mathematical Society