The pseudo-differential approach to finite differences revisited

Peter A. Markowich*, Frederic Poupaud

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We systematically derive arbitrary-order finite difference discretizations of linear (pseudo-) differential problems by appropriately approximating the symbols of the (pseudo) differential operators in frequency space. The convergence (i.e., stability and consistency) analysis of the difference schemes is based directly on micro-local properties of the exact and approximating symbols. The analytical approach presented here sheds new light on the general philosophy of finite differences.

Original languageEnglish (US)
Pages (from-to)161-186
Number of pages26
Issue number3
StatePublished - 1999
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics


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