By using a theorem of Sturm type the authors show that the approximations obtained by truncating the asymptotic series for the real zeros of the Airy functions Ai (x) or Bi (x) are in fact lower and upper bounds. A lower bound for the zeros of the derivatives of these functions is also derived.

The aim of this paper is to present an efficient numerical procedure for solving linear second order Fredholm integro-differential equations. The scheme is based on B-spline collocation and cubature formulas. The analysis is accompanied by numerical examples. The results demonstrate reliability and efficiency of the proposed algorithm.

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