This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

中文翻译：

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带误差分析的Volterra–Fredholm积分方程的Chebyshev搭配处理

这项工作报告了一种使用移位的切比雪夫搭配（SCC）方法对Volterra-Fredholm积分方程（V-FIE）进行数值求解的搭配算法。提出了平移切比雪夫多项式的一些性质。然后，将这些特性与移位的高斯-切比雪夫节点一起用于将Volterra-Fredholm积分方程简化为矩阵方程的解。接下来，提出了该方法的误差分析。我们将该算法的结果与其他算法进行了比较，证明了该方法的准确性和潜在适用性。