Higher order approximations in the heat equation and the truncated moment problem

Yong Jung Kim, Wei Ming Ni

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we employ linear combinations of n heat kernels to approximate solutions to the heat equation. We show that such approximations are of order O(t(1/2p-2n+1/2)) in Lp-norm, 1 ≤ p ≤ ∞, as t → ∞. For positive solutions of the heat equation such approximations are achieved using the theory of truncated moment problems. For general sign-changing solutions these type of approximations are obtained by simply adding an auxiliary heat kernel. Furthermore, inspired by numerical computations, we conjecture that such approximations converge geometrically as n → ∞ for any fixed t > 0.

Original languageEnglish (US)
Pages (from-to)2241-2261
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume40
Issue number6
DOIs
StatePublished - 2009

Bibliographical note

Publisher Copyright:
© 2009 Society for Industrial and Applied Mathematics.

Keywords

  • Approximation of an integral formula
  • Asymptotics convergence rates
  • Heat equation
  • Heat kernel
  • Moments

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