In recent times, operational matrix methods become overmuch popular. Actually, we have many more operational matrix methods. In this study, a new remodeled method is offered to solve linear Fredholm–Volterra integro-differential equations (FVIDEs) with piecewise intervals using Chebyshev operational matrix method. Using the properties of the Chebyshev polynomials, the Chebyshev operational matrix method is used to reduce FVIDEs into a linear algebraic equations. Some numerical examples are solved to show the accuracy and validity of the proposed method. Moreover, the numerical results are compared with some numerical algorithm.

中文翻译：

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求解分段区间线性Fredholm-Volterra积分-微分方程的运算矩阵方法

近年来，运算矩阵方法变得越来越流行。实际上，我们还有更多的运算矩阵方法。在这项研究中，提供了一种新的重构方法，可以使用Chebyshev运算矩阵方法以分段间隔求解线性Fredholm-Volterra积分微分方程（FVIDEs）。利用切比雪夫多项式的性质，使用切比雪夫运算矩阵方法将FVIDE简化为线性代数方程。数值算例表明了该方法的正确性和有效性。此外，将数值结果与一些数值算法进行了比较。