skip to main content
research-article

Single Step Methods and Low Order Splines for Solutions of Ordinary Differential Equations

Published: 01 March 1971 Publication History

Abstract

A procedure for obtaining low order, high accuracy spline function approximations for solutions of the initial value problem in ordinary differential equations is presented. The method is a single step method of order m. The spline is of class $C^1 $, but of degree m. The method is convergent for arbitrarily large m.

References

[1]
Peter Henrici, Discrete variable methods in ordinary differential equations, John Wiley & Sons Inc., New York, 1962xi+407
[2]
Frank R. Loscalzo, Thomas D. Talbot, Spline function approximations for solutions of ordinary differential equations, Bull. Amer. Math. Soc., 73 (1967), 438–442
[3]
Frank R. Loscalzo, Thomas D. Talbot, Spline function approximations for solutions of ordinary differential equations, SIAM J. Numer. Anal., 4 (1967), 433–445
[4]
F. R. Loscalzo, I. J. Schoenberg, On the use of spline functions for the approximation of solutions of ordinary differential equations, Tech. Summary Rep., 723, Mathematics Research Center, U.S: Army, University of Wisconsin, Madison, 1967
[5]
Frank R. Loscalzo, T. N. E. Greville, An introduction to the application of spline functions to initial value problems, Theory and Applications of Spline Functions (Proceedings of Seminar, Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1968), Academic Press, New York, 1969, 37–64

Index Terms

  1. Single Step Methods and Low Order Splines for Solutions of Ordinary Differential Equations
          Index terms have been assigned to the content through auto-classification.

          Recommendations

          Comments

          Information & Contributors

          Information

          Published In

          cover image SIAM Journal on Numerical Analysis
          SIAM Journal on Numerical Analysis  Volume 8, Issue 1
          Mar 1971
          177 pages
          ISSN:0036-1429
          DOI:10.1137/sjnaam.1971.8.issue-1
          Issue’s Table of Contents

          Publisher

          Society for Industrial and Applied Mathematics

          United States

          Publication History

          Published: 01 March 1971

          Qualifiers

          • Research-article

          Contributors

          Other Metrics

          Bibliometrics & Citations

          Bibliometrics

          Article Metrics

          • 0
            Total Citations
          • 0
            Total Downloads
          • Downloads (Last 12 months)0
          • Downloads (Last 6 weeks)0
          Reflects downloads up to 21 Sep 2024

          Other Metrics

          Citations

          View Options

          View options

          Get Access

          Login options

          Media

          Figures

          Other

          Tables

          Share

          Share

          Share this Publication link

          Share on social media