The number of boundary conditions for initial boundary value problems

Jan Nordstrom, Thomas M. Hagstrom

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Both the energy method and the Laplace transform method are frequently used for determining the number of boundary conditions required for a well posed initial boundary value problem. We show that these two distinctly different methods yield the same results. The continuous energy method can be mimicked exactly in the corresponding semidiscrete problems discretized using the summation-by-parts technique. Hence the analysis of well posedness and stability can bypass the more unwieldy Laplace transform method.

Original languageEnglish
Pages (from-to)2818-2828
Number of pages11
JournalSIAM Journal on Numerical Analysis
Issue number5
Publication statusPublished - Oct 2020


  • Boundary conditions
  • Energy method
  • Incompletely parabolic
  • Initial boundary value problems
  • Laplace transform method
  • Normal mode analysis
  • Summation-by-parts

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'The number of boundary conditions for initial boundary value problems'. Together they form a unique fingerprint.

Cite this