MODIFIED COLLOCATION METHODS FOR SECOND KIND OF VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR HIGHLY OSCILLATORY BESSEL KERNELS

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI:10.11948/20220559

Jianyu Wang, Chunhua Fang, Guifeng Zhang, Zaiyun Zhang

引用次数: 0

Abstract

In this paper, we investigate the second kind of Volterra integral equations with weakly sinular highly oscillatory Bessel kernels by using two collocation methods: direct high-order interpolationorder (DO) and direct Hermite interpolation (DH). Based on hypergeometric and Gamma functions, we obtain a method for solving the modified moments $ \int_{0}^{1}x^{\alpha}(1-x)^{\beta}J_{v}(\omega x)dx $. Compared with the Filon-type $ (Q_{N}^{F}) $ method, piecewise constant collocation $ (Q_{N}^{L, 0}) $ method and linear collocation $ (Q_{N}^{L, 1}) $ method, we verified the efficiency of the method through error analysis and numerical examples.

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一类具有弱奇异高振荡贝塞尔核的第二类volterra积分方程的修正配位方法

本文利用直接高阶插值(DO)和直接Hermite插值(DH)两种配置方法，研究了具有弱奇异高振荡贝塞尔核的第二类Volterra积分方程。基于超几何函数和伽玛函数，我们得到了一种求解修正矩$ \int_{0}^{1}x^{\alpha}(1-x)^{\beta}J_{v}(\omega x)dx $的方法。与filon型$ (Q_{N}^{F}) $法、分段常数配置$ (Q_{N}^{L, 0}) $法和线性配置$ (Q_{N}^{L, 1}) $法进行比较，通过误差分析和数值算例验证了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Analysis and Computation MATHEMATICS, APPLIED-

CiteScore

2.30

自引率

9.10%

发文量

期刊介绍： The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.