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A new method for the solution of the Cauchy problem for parabolic equations

Authors:

John Moore,

Prentiss RobinsonAuthors Info & Claims

Communications of the ACM, Volume 15, Issue 12

Pages 1050 - 1052

https://doi.org/10.1145/361598.361622

Published: 01 December 1972 Publication History

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Abstract

partial differential equations. When the equations are defined in unbounded domains, as in the initial value (Cauchy) problem, the solution of the integral equation by the method of successive approximation has inherent advantages over other methods. Error bounds for the method are of order h^3/2 and h^7/2 (h is the increment size) depending on the finite difference approximations involved.

References

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Friedman, A. Partial Differential Equations of Parabolic Type. Prentice-Hall, Englewood Cliffs, N.J., 1964.

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Forsythe, G.E., and Warow, W.R. Finite-Difference Methods for Partial Differential Equations Wiley, New York, 1960.

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Hicks, J.S., and Wei, J. Numerical solution of parabolic partial differential equations with two-point boundary conditions by use of the method of lines. J. ACM, 14, 3 (July 1967), 549-562.

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Zafarullah, A. Application of the method of lines to parabolic partial differential equations with error estimates. J. ACM 17, 2 (Apr. 1970), 294-302.

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Bramble, J. Numerical Solution of Partial Differential Equations. Academic Press, New York, 1966.

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Robinson, P., and Moore, J. Solution of the stochastic control problem in unbounded domains. J. Franklin Institute (to appear).

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Brauer, F., and Nobel, J.A. The Qualitations Theory of Ordinary Differential Equations. Benjamin, New York, 1969, p. 31.

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Cited By

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Killingbeck J(1999)Microcomputer calculations in physicsReports on Progress in Physics10.1088/0034-4885/48/1/00248:1(53-99)Online publication date: 1-Jan-1999
https://doi.org/10.1088/0034-4885/48/1/002
Robinson PMoore J(1973)Solution of the Stochastic control problem in unbounded domainsJournal of the Franklin Institute10.1016/0016-0032(73)90163-4295:3(185-192)Online publication date: Mar-1973
https://doi.org/10.1016/0016-0032(73)90163-4

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Communications of the ACM Volume 15, Issue 12

Dec. 1972

117 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/361598

Editor:
M. Stuart Lynn
Rice Univ., Houston, TX

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1972

Published in CACM Volume 15, Issue 12

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Killingbeck J(1999)Microcomputer calculations in physicsReports on Progress in Physics10.1088/0034-4885/48/1/00248:1(53-99)Online publication date: 1-Jan-1999
https://doi.org/10.1088/0034-4885/48/1/002
Robinson PMoore J(1973)Solution of the Stochastic control problem in unbounded domainsJournal of the Franklin Institute10.1016/0016-0032(73)90163-4295:3(185-192)Online publication date: Mar-1973
https://doi.org/10.1016/0016-0032(73)90163-4

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References

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An exponentially-fitted method for singularly perturbed, one-dimensional, parabolic problems

Numerical method of estimating the blow-up time and rate of the solution of ordinary differential equations: an application to the blow-up problems of partial differential equations

Infinite-Dimensional Hamilton--Jacobi Equations and Dirichlet Boundary Control Problems of Parabolic Type

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