The initial-value problem for the equation $(tu_{t})_{t}=u_{xx}$
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 ${(t{u_t})_t} = {u_{xx}}$ with the value of $u$ prescribed for $t = 0$ has a unique solution satisfying a maximum principle. In addition, several numerical schemes for its solution are proposed.
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- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- E. C. Du Fort and S. P. Frankel, Stability conditions in the numerical treatment of parabolic differential equations, Math. Tables Aids Comput. 7 (1953), 135–152. MR 59077, DOI https://doi.org/10.1090/S0025-5718-1953-0059077-7
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Additional Information
Keywords:
Initial-value problem,
maximum principle,
difference equation,
variable mesh,
stability condition
Article copyright:
© Copyright 1970
American Mathematical Society
