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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Numerical solution of a parabolic free boundary problem arising in statistical decision theory
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by Gary G. Sackett PDF
Math. Comp. 25 (1971), 425-434 Request permission

Abstract:

A parabolic free boundary problem which arises in a statistical decision setting is reduced to a free boundary problem for the heat equation which is amenable to numerical solution by the method of lines. An algorithm is given and the apparently globally converging results are compared with the asymptotic expansions of H. Chernoff and J. Breakwell.
References
  • John Breakwell and Herman Chernoff, Sequential tests for the mean of a normal distribution. II. (Large $t$), Ann. Math. Statist. 35 (1964), 162–173. MR 158456, DOI 10.1214/aoms/1177703738
  • Herman Chernoff, Sequential tests for the mean of a normal distribution, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I, Univ. California Press, Berkeley, Calif., 1961, pp.Β 79–91. MR 0131941
  • Herman Chernoff, Sequential tests for the mean of a normal distribution. III. (Small $t$), Ann. Math. Statist. 36 (1965), 28–54. MR 170442, DOI 10.1214/aoms/1177700269
    • Nguyen Dinh Chi (Thi), β€œOn a free boundary problem for a parabolic equation,” Vestnik Moskov. Univ. Ser. Math. Mech., No. 2, 1966, pp. 40-54. (Russian)
  • Erich Rothe, Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben, Math. Ann. 102 (1930), no.Β 1, 650–670 (German). MR 1512599, DOI 10.1007/BF01782368
  • Gary G. Sackett, An implicit free boundary problem for the heat equation, SIAM J. Numer. Anal. 8 (1971), 80–96. MR 283423, DOI 10.1137/0708011
    • B. Sherman, Some Comments on Free Boundary Problems for Parabolic Equations Arising in Statistical Decision Theory, Rocketdyne Research Report #66-24, 1966.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 425-434
  • MSC: Primary 65N35
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0300473-9
  • MathSciNet review: 0300473