Block boundary value methods for linear weakly singular Volterra integro-differential equations
Block boundary value methods for linear weakly singular Volterra integro-differential equations
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DOI：
10.1007/s10543-020-00840-1
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发表时间：
2021-03
影响因子：
1.5
通讯作者：
Yongtao Zhou;M. Stynes
中科院分区：
文献类型：
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作者：
Yongtao Zhou;M. Stynes
针对线性弱奇异Volterra积分微分方程组(VIDES)，构造了一类块边值方法。分析了这些方法的收敛和稳定性。结果表明，采用特殊的梯度网格可以获得最优的收敛速度。数值算例说明了理论结果的精确性和方法的计算有效性。此外，还给出了与VIDES的分段多项式配置法的数值比较，结果表明BBVM在数值精度上是相当的。
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.