Analytical Expansions for Parabolic Equations

24 Pages Posted: 14 Dec 2013 Last revised: 28 Nov 2014

See all articles by Matthew Lorig

Matthew Lorig

University of Washington - Applied Mathematics

Stefano Pagliarani

DEAMS, Università di Trieste

Andrea Pascucci

University of Bologna - Department of Mathematics

Date Written: November 27, 2014

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.

Keywords: parabolic PDE, asymptotic expansion, singular perturbation, analytical approximation

JEL Classification: C00

Suggested Citation

Lorig, Matthew and Pagliarani, Stefano and Pascucci, Andrea, Analytical Expansions for Parabolic Equations (November 27, 2014). Available at SSRN: https://ssrn.com/abstract=2366864 or http://dx.doi.org/10.2139/ssrn.2366864

Matthew Lorig (Contact Author)

University of Washington - Applied Mathematics ( email )

Seattle, WA
United States

Stefano Pagliarani

DEAMS, Università di Trieste ( email )

Via Valerio n. 4/1
Trieste
Italy

HOME PAGE: http://www.cmap.polytechnique.fr/~pagliarani/

Andrea Pascucci

University of Bologna - Department of Mathematics ( email )

Piazzadi Porta San Donato, 5
Bologna, 40126
Italy

HOME PAGE: http://www.dm.unibo.it/~pascucci

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