Abstract
It is proposed to extend Dzyadyk's approximation method (the a-method) for approximating solutions of linear ordinary differential equations with polynomial coefficients by algebraic polynomials to solve integral equations of the Volterra-Urysohn type with polynomial non-linearities. A suitable scheme is presented and error estimates are established for the a-method in the metrics of spaces of continuous functions and square-integrable functions with a Chebyshev weight function.
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