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

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 and D. Hilbert,*Methods of mathematical physics. Vol. I*, Interscience Publishers, Inc., New York, N.Y., 1953. MR**0065391****[2]**R. Courant and D. Hilbert,*Methods of mathematical physics. Vol. I*, Interscience Publishers, Inc., New York, N.Y., 1953. MR**0065391****[3]**E. C. Du Fort and S. P. Frankel,*Stability conditions in the numerical treatment of parabolic differential equations*, Math. Tables and Other Aids to Computation**7**(1953), 135–152. MR**0059077**, 10.1090/S0025-5718-1953-0059077-7**[4]**E. E. Zajac,*Note on overly-stable difference approximations*, J. Math. and Phys.**43**(1964), 51-54. MR**0162372**

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Additional Information

DOI:
http://dx.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