We consider the Cauchy problem associated with a general parabolic partial differential equation in d dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping technique, we also provide convergence results for arbitrarily large time intervals.
Lorig M., Pagliarani S., Pascucci A. (2015). Analytical expansions for parabolic equations. SIAM JOURNAL ON APPLIED MATHEMATICS, 75(2), 468-491 [10.1137/130949968].
Analytical expansions for parabolic equations
Pagliarani S.;PASCUCCI, ANDREA
2015
Abstract
We consider the Cauchy problem associated with a general parabolic partial differential equation in d dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping technique, we also provide convergence results for arbitrarily large time intervals.File in questo prodotto:
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