Analytical Expansions for Parabolic Equations
24 Pages Posted: 14 Dec 2013 Last revised: 28 Nov 2014
Date Written: November 27, 2014
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.
Keywords: parabolic PDE, asymptotic expansion, singular perturbation, analytical approximation
JEL Classification: C00
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