Boundary conditions for multistep finite-difference methods for time-dependent equations

David Gottlieb*, Eli Turkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The stability and accuracy of various boundary treatments are analyzed for the two-step Richtmyer and MacCormack methods. Special attention is paid to ways of imposing the extra boundary conditions after the first step of the two-step process. The theory of Kreiss is used to study stability properties for both scalar and vector equations. The theory of Skollermo is used to compare accuracies of the various methods. Computations were also performed on both wavelike equations and on systems that approach a steady state. Several suggestions are given for more reliable boundary treatments.

Original languageEnglish
Pages (from-to)181-196
Number of pages16
JournalJournal of Computational Physics
Issue number2
StatePublished - Feb 1978
Externally publishedYes


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