具有多尺度和非线性指数核的Volterra积分方程的高阶光滑性与高阶配点逼近
High-order smoothness and high-order collocation approximation for Volterra integral equation with multiscale and nonlinear exponent kernel
- Yunnan Normal University（云南师范大学）
- Shandong University（山东大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对具有多尺度和非线性指数核的Volterra积分方程，提出高阶光滑性条件消除初始奇异性，并开发了任意多项式次数的配点方法，扩展了现有工作。
AI中文摘要：
我们考虑一个具有多尺度和非线性指数核的Volterra积分方程。我们提出了高阶光滑性条件，在这些条件下，解的初始奇异性可以被消除到任意指定的阶数。这表明了核的多尺度性质在解的局部修正中的应用。然后，基于解的正则性，在均匀或分级网格上开发并分析了一种具有任意多项式次数的不连续高阶配点方法。这项工作在数学和数值方面都是对[Zheng, Qiu and Stynes, SIAM J. Numer. Anal., to appear]的全面扩展和补充。
英文摘要：
We consider a Volterra integral equation with multiscale and nonlinear exponent kernel. We propose the high-order smoothing conditions, under which the initial singularity of the solutions can be eliminated up to any prescribed order. This indicates the application of the multiscale nature of the kernel on local modification of the solutions. Then a discontinuous high-order collocation method with arbitrary polynomial degree is developed and analyzed on uniform or graded meshes based on the solution regularity. This work serves as a comprehensive extension and complement to [Zheng, Qiu and Stynes, SIAM J. Numer. Anal., to appear] in both mathematical and numerical aspects.
