Skip to main content
SpringerLink
Log in

On 3-stage geometric explicit Runge–Kutta method for singular autonomous initial value problems in ordinary differential equations

  • Published:
Computing Aims and scope Submit manuscript

Abstract

There has been considerable efforts to increase the efficiency of explicit Runge–Kutta (ERK) methods over the years. However, this always lead to increase in the number of terms of the Taylors’ series incremental function. In this work, a 3-stage geometric explicit Runge–Kutta method for solving autonomous initial value problems in ordinary differential equations is derived and implemented. The computational results show that the method is stable, efficient and accurate. We also compared this method with some other conventional methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dalquist G, Bjorck A (1774) Numerical methods. Prentice-Hall, Englewood Cliffs

  2. Euler H (1768) Institutiones calculi integralis. Volumen Primum, Opera Omnia, vol XI, B. G. Teubneri Lipsiae et Berolini MCMXIII

  3. Euler L (1913) De integratione aequationum differentialium per approximationem. In: Opera Omnia, 1st series, vol 11, Institutiones Calculi Integralis. Teubner, Leipzig, pp 424–434

  4. Fatunla SO (1988) Numerical methods for IVPs in ODEs. Academic Press, New York

    Google Scholar 

  5. Lambert JD (1973) Computational methods in ODEs. Wiley, New York

    Google Scholar 

  6. Lambert JD (1991) Numerical methods for ordinary differential systems: the initial value problem. Wiley, Chichester

    MATH  Google Scholar 

  7. Lee JHJ (2004) Numerical methods for ordinary differential systems: a survey of some standard methods. MSc thesis, University of Auckland, Auckland

  8. Lotkin W (1951) On the accuracy of Runge–Kutta’s methods. MTAC 5: 128–132

    MathSciNet  MATH  Google Scholar 

  9. Runge C (1895) Uber die numerische Auflosung von differntialglechungen. Math Ann 46: 167–178

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Lagos State University, Lagos, Nigeria

    Moses Adebowale Akanbi

Authors
  1. Moses Adebowale Akanbi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moses Adebowale Akanbi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Akanbi, M.A. On 3-stage geometric explicit Runge–Kutta method for singular autonomous initial value problems in ordinary differential equations. Computing 92, 243–263 (2011). https://doi.org/10.1007/s00607-010-0139-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00607-010-0139-3

Keywords

Mathematics Subject Classification (2000)

Search

Navigation