Fourth-order finite-difference methods for two-point boundary-value problems

E. A. Bogucz, J. D.A. Walker

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A number of new fourth-order accurate finite-difference methods are developed for second-order ordinary differential equations of the boundary-value type. Schemes are obtained for both linear and non-linear equations. In all cases, the solution of the difference equations may be accomplished using a direct elimination technique for linear tridiagonal matrix problems. The accuracy of the new methods is compared with existing finite-difference methods on a theoretical basis as well as by considering a number of example problems. It is concluded that the new methods offer significant advantages for specific types of equations in terms of accuracy and/or computational efficiency.

Original languageEnglish (US)
Pages (from-to)69-82
Number of pages14
JournalIMA Journal of Numerical Analysis
Issue number1
StatePublished - Jan 1984
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Computational Mathematics
  • Applied Mathematics


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