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Mathematics of Computation

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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: 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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Keywords: Initial-value problem, maximum principle, difference equation, variable mesh, stability condition
Article copyright: © Copyright 1970 American Mathematical Society