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The initial-value problem for the equation $ (tu\sb{t})\sb{t}=u\sb{xx}$

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: 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