Solution of general ordinary differential equations using the algebraic theory approach

Michael Celia, Ismael Herrera

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

The algebraic theory for numerical methods, as developed by Herrera [3–7], provides a broad theoretical framework for the development and analysis of numerical approximations. To this point, the technique has only been applied to ordinary differential equations with constant coefficients. The present work extends the theory by developing a methodology for equations with variable coefficients. Approximation of the coefficients by piecewise polynomials forms the foundation of the approach. Analysis of the method provides firm error estimates. Furthermore, the analysis points to particular procedures that produce optimal accuracy. Example calculations illustrate the computational procedure and verify the theoretical convergence rates.

Original languageEnglish (US)
Pages (from-to)117-129
Number of pages13
JournalNumerical Methods for Partial Differential Equations
Volume3
Issue number2
DOIs
StatePublished - 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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