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

R. Parvaz (), M. Zarebnia () and A. Saboor Bagherzadeh ()
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R. Parvaz: University of Mohaghegh Ardabili
M. Zarebnia: University of Mohaghegh Ardabili
A. Saboor Bagherzadeh: Ferdowsi University of Mashhad

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 1203-1223

Abstract: 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.

Keywords: Deviation of the error; collocation; finite difference; exact finite difference; integro-differential; 41A25; 45J05; 65N35 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0459-8

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