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A Study of Error Estimation for Second Order Fredholm Integro-Differential Equations

Author

Listed:
  • R. Parvaz

    (University of Mohaghegh Ardabili)

  • M. Zarebnia

    (University of Mohaghegh Ardabili)

  • A. Saboor Bagherzadeh

    (Ferdowsi University of Mashhad)

Abstract

In this work, we study efficient asymptotically correct a posteriori error estimates for the numerical approximation of second order Fredholm integro-differential equations. We use the defect correction principle to find the deviation of the error estimation and show that collocation method by using m degree piecewise polynomial provides order $$\mathcal{O}(h^{m+2})$$ O ( h m + 2 ) for the deviation of the error. Also, the theoretical behavior is tested on examples and it is shown that the numerical results confirm theoretical analysis.

Suggested Citation

  • R. Parvaz & M. Zarebnia & A. Saboor Bagherzadeh, 2020. "A Study of Error Estimation for Second Order Fredholm Integro-Differential Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 1203-1223, September.
  • Handle: RePEc:spr:indpam:v:51:y:2020:i:3:d:10.1007_s13226-020-0459-8
    DOI: 10.1007/s13226-020-0459-8
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