具有高振荡贝塞尔核的 Volterra 积分方程的正交方法

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-09-05 DOI:10.1016/j.matcom.2024.09.002

Longbin Zhao , Pengde Wang , Qiongqi Fan

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引用次数: 0

摘要

为了避免计算矩，本研究采用广义正交法来求解具有高振荡贝塞尔核的 Volterra 积分方程。首先，我们在回顾正交方法的构造后，详细研究了区间长度和频率的影响。然后，对方程采用两点正交法。通过估计权重，我们可以保证离散方程是可解的。在收敛性方面，我们的分析表明，所提出的方法具有 5/2 的渐近阶，随着 h 的减小，其收敛阶数也为 2。在数值部分，我们提供了一些数值示例来检验该方法。

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A quadrature method for Volterra integral equations with highly oscillatory Bessel kernel

To avoid computing moments, this work adopts generalized quadrature method for Volterra integral equations with highly oscillatory Bessel kernel. At first, we study the influence of the interval length and frequency in detail after recalling the construction of the quadrature method. Then, the two-point quadrature method is employed for the equation. By estimating the weights, we could guarantee that the discretized equation is solvable. For its convergence, our analysis shows that the proposed method enjoys asymptotic order $5 / 2$ and as $h$ decreases it converges with order 2 as well. Some numerical illustrations are provided to test the method in the numerical part.

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.