Skip to main content

Nonlinear Volterra Integro-Differential Equations

  • Chapter
Linear and Nonlinear Integral Equations

Abstract

It is well known that linear and nonlinear Volterra integral equations arise in many scientific fields such as the population dynamics, spread of epidemics, and semi-conductor devices. Volterra started working on integral equations in 1884, but his serious study began in 1896. The name integral equation was given by du Bois-Reymond in 1888.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Abdelkhani, Higher order methods for solving Volterra integro-differential equations of the first kind, Appl. Math. Comput., 57 (1993) 97–101.

    Article  MathSciNet  Google Scholar 

  2. P. Linz, A simple approximation method for solving Volterra integro-differential equations of the first kind, J. Inst. Math. Appl., 14 (1974) 211–215.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Linz, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, (1985).

    Book  MATH  Google Scholar 

  4. C. Baker, The Numerical Treatment of Integral Equations, Oxford University Press, London, (1977).

    MATH  Google Scholar 

  5. H.T. Davis, Introduction to Nonlinear Differential and Integral Equations, Dover, Publications, New York, (1962).

    MATH  Google Scholar 

  6. A. Jerri, Introduction to Integral Equations with Applications, Wiley, New York, (1999).

    MATH  Google Scholar 

  7. R.K. Miller, Nonlinear Volterra Integral Equations, W.A. Benjamin, Menlo Park, CA, (1967).

    Google Scholar 

  8. K. Maleknejad and Y. Mahmoudi, Taylor polynomial solution of high-order nonlinear Volterra-Fredholm integro-differential equations, Appl. Math. Comput. 145 (2003) 641–653.

    Article  MathSciNet  MATH  Google Scholar 

  9. W.E. Olmstead and R.A. Handelsman, Asymptotic solution to a class of nonlinear Volterra integral equations, II, SIAM J. Appl. Math., 30 (1976) 180–189.

    Article  MathSciNet  MATH  Google Scholar 

  10. A.M. Wazwaz, A First Course in Integral Equations, World Scientific, Singapore, (1997).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Wazwaz, AM. (2011). Nonlinear Volterra Integro-Differential Equations. In: Linear and Nonlinear Integral Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21449-3_14

Download citation

Publish with us

Policies and ethics