The initial-value problem for the equation

Authors:
Alan Solomon and Faiza Solomon

Journal:
Math. Comp. **24** (1970), 611-620

MSC:
Primary 65.67; Secondary 35.00

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273847-1

MathSciNet review:
0273847

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the initial-value problem of the equation with the value of prescribed for has a unique solution satisfying a maximum principle. In addition, several numerical schemes for its solution are proposed.

**[1]**R. Courant & D. Hilbert,*Methods of Mathematical Physics.*Vol. I, Interscience, New York, 1953. MR**16**, 426. MR**0065391 (16:426a)****[2]**R. Courant & D. Hilbert,*Methods of Mathematical Physics.*Vol. II, Interscience, New York, 1962. MR**25**#4216. MR**0065391 (16:426a)****[3]**E. DuFort & S. Frankel, "Stability conditions in the numerical treatment of parabolic differential equations,"*Math. Tables and Other Aids to Computation*, v. 7, 1953, pp. 135-152. MR**15**, 474. MR**0059077 (15:474a)****[4]**E. Zajac, "Note on overly-stable difference approximations,"*J. Math, and Phys.*, v. 43, 1964, pp. 51-54. MR**28**#5571. MR**0162372 (28:5571)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0273847-1

Keywords:
Initial-value problem,
maximum principle,
difference equation,
variable mesh,
stability condition

Article copyright:
© Copyright 1970
American Mathematical Society