An optimum implicit recurrence formula for the heat conduction equation
Author:
Stephen H. Crandall
Journal:
Quart. Appl. Math. 13 (1955), 318-320
MSC:
Primary 65.0X
DOI:
https://doi.org/10.1090/qam/73292
MathSciNet review:
73292
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E. Schmidt, Über die Andwendung der Differenzenrechnung auf technische Anheiz-und-Abkühungsprobleme, A. Föppl Festschrift, Springer, Berlin, 1924, pp. 179-189
- J. Crank and P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Proc. Cambridge Philos. Soc. 43 (1947), 50–67. MR 19410
- George G. O’Brien, Morton A. Hyman, and Sidney Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics 29 (1951), 223–251. MR 0040805
- William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR 0068321
- Clarence M. Fowler, Analysis of numerical solutions of transient heat-flow problems, Quart. Appl. Math. 3 (1946), 361–376. MR 15190, DOI https://doi.org/10.1090/S0033-569X-1946-15190-X
- Stephen H. Crandall, Implicit vs. explicit recurrence formulas for the linear diffusion equation, J. Assoc. Comput. Mach. 2 (1955), 42–49. MR 68911, DOI https://doi.org/10.1145/320789.320794
See, for example, F. B. Hildebrand, Methods of applied mathematics, Prentice-Hall, N. Y., 1952, p. 330
For six possible alternatives see P. H. Price and M. R. Slack, Stability and accuracy of numerical solutions of the heat flow equation, Brit. J. Appl. Phys. 3, 379-384 (1952)
E. Schmidt, Über die Andwendung der Differenzenrechnung auf technische Anheiz-und-Abkühungsprobleme, A. Föppl Festschrift, Springer, Berlin, 1924, pp. 179-189
J. Crank and P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of heat-conduction type, Proc. Camb. Phil. Soc. 32, 50-67 (1947)
G. G. O’Brien, M. A. Hyman and S. Kaplan, A study of the numerical solution of partial differential equations, J. Math. Phys. 29, 223-251 (1951)
W. E. Milne, Numerical solution of differential equations, John Wiley, N. Y., 1953, p. 122
C. M. Fowler, Analysis of numerical solutions of transient heat-flow problems, Quart. Appl. Math. 3, 361-376 (1946)
S. H. Crandall, Implicit vs. explicit recurrence formulas for the linear diffusion equation. J. Assoc. Comput. Mach. 2, 42-49 (1955)
See, for example, F. B. Hildebrand, Methods of applied mathematics, Prentice-Hall, N. Y., 1952, p. 330
For six possible alternatives see P. H. Price and M. R. Slack, Stability and accuracy of numerical solutions of the heat flow equation, Brit. J. Appl. Phys. 3, 379-384 (1952)
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© Copyright 1955
American Mathematical Society