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 \(\mathcal{O}(h^{m+2})\) 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.
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We would like to thank the anonymous referees for their valuable comments and suggestions, which helped improve the original manuscript of this paper.
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Parvaz, R., Zarebnia, M. & Bagherzadeh, A.S. A Study of Error Estimation for Second Order Fredholm Integro-Differential Equations. Indian J Pure Appl Math 51, 1203–1223 (2020). https://doi.org/10.1007/s13226-020-0459-8
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DOI: https://doi.org/10.1007/s13226-020-0459-8