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Time discretization in the backward solution of parabolic equations. II

Author: Lars Eldén
Journal: Math. Comp. 39 (1982), 69-84
MSC: Primary 65M30
MathSciNet review: 658214
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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 and L. Nirenberg, Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math. 16 (1963), 121–239. MR 0155203
  • [2] B. L. Buzbee and Alfred Carasso, On the numerical computation of parabolic problems for preceding times, Math. Comp. 27 (1973), 237–266. MR 0368448, 10.1090/S0025-5718-1973-0368448-3
  • [3] B. L. Buzbee, Application of fast Poisson solvers to 𝐴-stable marching procedures for parabolic problems, SIAM J. Numer. Anal. 14 (1977), no. 2, 205–217. MR 0436613
  • [4] Lars Eldén, Regularization of the backward solution of parabolic problems, Inverse and improperly posed problems in differential equations (Proc. Conf., Math. Numer. Methods, Halle, 1979) Math. Res., vol. 1, Akademie-Verlag, Berlin, 1979, pp. 73–81. MR 536169
  • [5] L. Eldén, "Time discretization in the backward solution of parabolic equations. I," Math. Comp., v. 39, 1982, pp.
  • [6] Avner Friedman, Partial differential equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969. MR 0445088
  • [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, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. Regional Conference Series in Applied Mathematics, No. 22. MR 0463736
  • [9] V. N. Strakhov, "Solution of incorrectly-posed linear problems in Hilbert space," Differential Equations, v. 6, 1970, pp. 1136-1140. (Russian)

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Article copyright: © Copyright 1982 American Mathematical Society