A direct numerical procedure for the Cauchy problem for the heat equation
β Scribed by J.R Cannon; Richard E Ewing
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 427 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0022-247X
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## Abstract The nonβcharacteristic Cauchy problem for the heat equation __u__~__xx__~(__x__,__t__) = __u__~1~(__x__,__t__), 0 β©½ __x__ β©½ 1, β β < __t__ < β, __u__(0,__t__) = Ο(__t__), __u__~__x__~(0, __t__) = Ο(__t__), β β < __t__ < β is regularizΓ¨d when approximate expressions for Ο and Ο are given
## Abstract Let __D__ β β^__n__^ be a bounded domain with piecewiseβsmooth boundary, and __q__(__x__,__t__) a smooth function on __D__ Γ [0, __T__]. Consider the timeβlike Cauchy problem magnified image magnified image Given __g__, __h__ for which the equation has a solution, we show how to approxi