Time discretization in the backward solution of parabolic equations. II
Author:
Lars Eldén
Journal:
Math. Comp. 39 (1982), 6984
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.
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 [2]
 B. L. Buzbee & A. Carasso, "On the numerical computation of parabolic problems for preceding times," Math. Comp., v. 27, 1973, pp. 237266. MR 0368448 (51:4689)
 [3]
 B. L. Buzbee, "Applications of fast Poisson solvers to Astable marching procedures for parabolic problems," SIAM J. Numer. Anal., v. 14, 1977, pp. 205217. MR 0436613 (55:9556)
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 L. Eldén, "Regularization of the backward solution of parabolic problems," Inverse and Improperly Posed Problems in Differential Equations (G. Anger, ed.), AkademieVerlag, Berlin, 1979. MR 536169 (80e:65109)
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 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. 4665. (Russian)
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 L. E. Payne, Improperly Posed Problems in Partial Differential Equations, SIAM, Philadelphia, Pa., 1975. MR 0463736 (57:3678)
 [9]
 V. N. Strakhov, "Solution of incorrectlyposed linear problems in Hilbert space," Differential Equations, v. 6, 1970, pp. 11361140. (Russian)
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DOI:
http://dx.doi.org/10.1090/S0025571882998428
PII:
S 00255718(82)998428
Article copyright:
© Copyright 1982
American Mathematical Society
