Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

Time discretization in the backward solution of parabolic equations. II


Author: Lars Eldén
Journal: Math. Comp. 39 (1982), 69-84
MSC: Primary 65M30
DOI: https://doi.org/10.1090/S0025-5718-82-99842-8
MathSciNet review: 658214
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The backward beam method for solving a parabolic partial differential equation backward in time is studied.

Time discretizations based on Padé approximations of the exponential function are considered, and a priori estimates of the step length are given, which guarantee an almost optimal error bound. The computational efficiency of different discretizations is discussed. Some numerical examples are given, which compare the backward beam method and the regularization method studied in Part I of this paper.


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

  • [1] S. Agmon & L. Nirenberg, "Properties of solutions of ordinary differential equations in Banach space," Comm. Pure Appl. Math., v. 16, 1963, pp. 121-239. MR 0155203 (27:5142)
  • [2] B. L. Buzbee & A. Carasso, "On the numerical computation of parabolic problems for preceding times," Math. Comp., v. 27, 1973, pp. 237-266. MR 0368448 (51:4689)
  • [3] B. L. Buzbee, "Applications of fast Poisson solvers to A-stable marching procedures for parabolic problems," SIAM J. Numer. Anal., v. 14, 1977, pp. 205-217. MR 0436613 (55:9556)
  • [4] L. Eldén, "Regularization of the backward solution of parabolic problems," Inverse and Improperly Posed Problems in Differential Equations (G. Anger, ed.), Akademie-Verlag, Berlin, 1979. MR 536169 (80e:65109)
  • [5] L. Eldén, "Time discretization in the backward solution of parabolic equations. I," Math. Comp., v. 39, 1982, pp.
  • [6] A. Friedman, Partial Differential Equations, Holt, Rinehart, and Winston, New York, 1969. MR 0445088 (56:3433)
  • [7] V. A. Morozov, "On the restoration of functions with guaranteed accuracy," Numerical Analysis in Fortran, Moscow Univ. Press, Moscow, 1979, pp. 46-65. (Russian)
  • [8] L. E. Payne, Improperly Posed Problems in Partial Differential Equations, SIAM, Philadelphia, Pa., 1975. MR 0463736 (57:3678)
  • [9] V. N. Strakhov, "Solution of incorrectly-posed linear problems in Hilbert space," Differential Equations, v. 6, 1970, pp. 1136-1140. (Russian)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M30

Retrieve articles in all journals with MSC: 65M30


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-82-99842-8
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society