The approximation of solutions to initial boundary value problems for parabolic equations in one space variable
Author:
David Colton
Journal:
Quart. Appl. Math. 33 (1976), 377-386
MSC:
Primary 35K15; Secondary 35C15
DOI:
https://doi.org/10.1090/qam/454348
MathSciNet review:
454348
Full-text PDF Free Access
References |
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Additional Information
- Stefan Bergman, The approximation of functions satisfying a linear partial differential equation, Duke Math. J. 6 (1940), 537–561. MR 3328
- Stefan Bergman and John G. Herriot, Numerical solution of boundary-value problems by the method of integral operators, Numer. Math. 7 (1965), 42–65. MR 176619, DOI https://doi.org/10.1007/BF01397972
- David Colton, Integral operators and reflection principles for parabolic equations in one space variable, J. Differential Equations 15 (1974), 551–559. MR 338539, DOI https://doi.org/10.1016/0022-0396%2874%2990073-4
A. Erdléyi et al., Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953
- P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
- R. P. Gilbert, Integral operator methods for approximating solutions of Dirichlet problems, Iterationsverfahren, Numerische Mathematik, Approximationstheorie (Tagung Numer. Method. Approximationstheorie, Oberwolfach, 1969) Birkhäuser, Basel, 1970, pp. 129–146. Internat. Schriftenreihe Numer. Math., Vol. 15. With an appendix by Kendall E. Atkinson. MR 0380076
- Günter Hellwig, Partial differential equations: An introduction, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. Translated by E. Gerlach. MR 0173071
- E. M. Landis, Some questions in the qualitative theory of elliptic and parabolic equations, Amer. Math. Soc. Transl. (2) 20 (1962), 173–238. MR 0136855, DOI https://doi.org/10.1090/trans2/020/05
- P. C. Rosenbloom and D. V. Widder, Expansions in terms of heat polynomials and associated functions, Trans. Amer. Math. Soc. 92 (1959), 220–266. MR 107118, DOI https://doi.org/10.1090/S0002-9947-1959-0107118-2
- N. L. Schryer, Constructive approximation of solutions to linear elliptic boundary value problems, SIAM J. Numer. Anal. 9 (1972), 546–572. MR 321327, DOI https://doi.org/10.1137/0709050
- F. G. Tricomi, Integral equations, Pure and Applied Mathematics, Vol. V, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1957. MR 0094665
- D. V. Widder, Analytic solutions of the heat equation, Duke Math. J. 29 (1962), 497–503. MR 157127
S. Bergman, The approximation of functions satisfying a linear partial differential equation, Duke. Math. J. 6, 537–561 (1940)
S. Bergman and J. G. Herriot, Numerical solution of boundary value problems by the method of integral operators, Numer. Math. 7, 42–65 (1965)
D. Colton, Integral operators and reflection principles for parabolic equations in one space variable, J. Diff. Eqns. 15, 551–559 (1974)
A. Erdléyi et al., Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953
P. Garabedian, Partial differential equations, John Wiley, New York, 1964
R. P. Gilbert, Integral operator methods for approximating solutions of Dirichlet problems, in Numerische Methoden der Approximationstheorie, Birkhauser Verlag, Basel, 1970
G. Hellwig, Partial differential equations, Blaisdell, New York, 1964
E. M. Landis, Some questions in the qualitative theory of elliptic and parabolic equations, in American Mathematical Society Translations, Series 2, Vol. 20, American Mathematical Society, Providence, 1962
P. C. Rosenbloom and D. V. Widder, Expansions in terms of heat polynomials and associated functions, Trans. Amer. Math. Soc. 92, 220–266 (1959)
N. L. Schryer, Constructive approximation of solutions to linear elliptic boundary value problems, SIAM J. Numer. Anal. 9, 546–572 (1972)
F. G. Tricomi, Integral equations, Interscience, New York, 1957
D. V. Widder, Analytic solutions of the heat equation, Duke Math. J. 29, 497–503 (1962)
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Article copyright:
© Copyright 1976
American Mathematical Society
