Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Semianalytic numerical studies of turning points arising in stiff boundary value problems


Authors: W. L. Miranker and J. P. Morreeuw
Journal: Math. Comp. 28 (1974), 1017-1034
MSC: Primary 65L10
DOI: https://doi.org/10.1090/S0025-5718-1974-0381329-5
MathSciNet review: 0381329
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation proceeds with mesh increments which are orders of magnitude larger than those used by other known methods.


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

  • [1] F. W. DORR, "An example of ill-conditioning in the numerical solution of singular perturbation problems," Math. Comp., v. 25, 1971, pp. 271-283. MR 0297142 (45:6200)
  • [2] F. W. DORR, S. V. PARTER & L. F. SHAMPINE, "Application of the maximum principle to singular perturbation problems," SIAM Rev., v. 15, 1972, pp. 43-88. MR 0320456 (47:8995)
  • [3] A. M. IL'IN, "A difference scheme for a differential equation with a small parameter multiplying the highest derivative," Mat. Zametki, v. 6, 1969, pp. 237-248 = Math. Notes, v. 6, 1969, pp. 596-602. MR 41 #4823. MR 0260195 (41:4823)
  • [4] W. L. MIRANKER, "Numerical methods of boundary layer type for stiff systems of ordinary differential equations," Computing, v. 11, 1973, pp. 221-234. MR 0386276 (52:7134)
  • [5] R. E. O'MALLEY, Introduction to Singular Perturbation, Lecture Notes at Edinburgh, Autumn, 1971.
  • [6] C. E. PEARSON, "On a differential equation of boundary layer type," J. Mathematical Phys., v. 47, 1968, pp. 134-154. MR 37 #3773. MR 0228189 (37:3773)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L10

Retrieve articles in all journals with MSC: 65L10


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1974-0381329-5
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society