We propose a numerical scheme based upon the Bernstein approximation method for computational solution of a new class of Volterra integral equations of the third kind (3rdVIEs). Construction of the technique and its practicality for proposed equations have been introduced. Furthermore we have examined the numerability and convergence analysis of the proposed scheme. Finally, we demonstrate a series of numerical examples demonstrating the effectiveness of this new technique for solving 3rdVIEs.

中文翻译：

---

第三类 Volterra 积分方程数值解的 Bernstein 近似技术

我们提出了一种基于 Bernstein 近似方法的数值方案，用于计算一类新的第三类 Volterra 积分方程 (3rdVIE)。介绍了该技术的构造及其对建议方程的实用性。此外，我们已经检查了所提出方案的可数性和收敛性分析。最后，我们展示了一系列数值例子，证明了这种新技术在解决 3rdVIE 方面的有效性。