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The main feature of this paper is an application of the modified Bernstein operator in the approximate and numerical solution of integral equations. The stability of the algorithm is discussed in the context of errors resulting from the numerical approximation of Volterra integral equations. The mechanism of the proposed method is explained in detail, including its main features. Furthermore, a comparison with an alternative numerical technique is made, and the superiority of the proposed solution is shown. Numerical experiments are also performed to verify the validity of the proposed method and to assess its accuracy. Finally, several conclusions are drawn from the results of the numerical experiments. The proposed method provides a powerful and efficient tool for the approximate solution of Volterra integral equations, and its results are promising. The results obtained from this algorithm are useful in the numerical analysis of integral equations. [ABSTRACT FROM AUTHOR]