重复中点法则用于第一类弱奇异Volterra积分方程的稳定解及其扰动数据
The repeated midpoint rule for weakly singular Volterra integral equations of the first kind with perturbed data
AI总结：
本文研究了重复中点法则在处理第一类弱奇异Volterra积分方程稳定解时的正则化性质，考虑了解及其导数的Hölder连续性，并通过修正权重消除初始条件的影响，最终给出数值结果。
摘要：
在本文中，我们考虑了重复中点法则在处理具有扰动右端项的第一类弱奇异Volterra积分方程稳定解时的正则化性质。仔细考虑了解及其导数的Hölder连续性，并考虑修正权重以消除初始条件。证明四次项权重的逆稳定性依赖于Banach代数技术。最后给出了数值结果。
英文摘要：
In the present paper we consider the regularizing properties of the repeated midpoint rule for the stable solution of weakly singular Volterra integral equations of the first kind with perturbed right hand sides. The Hölder continuity of the solution and its derivative is carefully taken into account, and correction weights are considered to get rid of initial conditions. The proof of the inverse stability of the quadrature weights relies on Banach algebra techniques. Finally, numerical results are presented.
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