Improvement of the piecewise polynomial collocation method for Fredholm integro-differential equations

Reza Parvaz; M.  Zarebnia; A. Saboor  Bagherzadeh

doi:10.5269/bspm.66195

Reza Parvaz University of Mohaghegh Ardabili
M. Zarebnia
A. Saboor Bagherzadeh

Résumé

In this work, in the first step,
the error estimation by using defect correction principle
is studied for
the numerical approximation of Fredholm integro-differential equations.
Based on theoretical study, it is shown that
for $m$ degree piecewise
polynomial collocation method, the deviation of the error is
$\mathcal{O}(h^{m+1})$.
In the next step by using the deviation of the error the collocation solution has been improved.
Also in the last step of this paper, simulated results to investigate the theory results are given.

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