The initial-value problem for the equation $(tu_{t})_{t}=u_{xx}$
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- by Alan Solomon and Faiza Solomon PDF
- Math. Comp. 24 (1970), 611-620 Request permission
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.References
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- 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 10.1090/S0025-5718-1953-0059077-7
- E. E. Zajac, Note on overly-stable difference approximations, J. Math. and Phys. 43 (1964), 51–54. MR 162372, DOI 10.1002/sapm196443151
Additional Information
- © Copyright 1970 American Mathematical Society
- 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