A class of block boundary value methods (BBVMs) is constructed for linear weakly singular Volterra integro-differential equations (VIDEs). The convergence and stability of these methods is analysed. It is shown that optimal convergence rates can be obtained by using special graded meshes. Numerical examples are given to illustrate the sharpness of our theoretical results and the computational effectiveness of the methods. Moreover, a numerical comparison with piecewise polynomial collocation methods for VIDEs is given, which shows that the BBVMs are comparable in numerical precision.

中文翻译：

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线性弱奇异Volterra积分微分方程的块边界值方法

针对线性弱奇异Volterra积分微分方程（VIDE），构造了一类块边界值方法（BBVM）。分析了这些方法的收敛性和稳定性。结果表明，通过使用特殊的渐变网格可以获得最佳收敛速度。数值算例说明了我们的理论结果的正确性和方法的计算有效性。此外，给出了与VIDE的分段多项式配置方法的数值比较，这表明BBVM在数值精度方面具有可比性。