Representative Publications： [1] Xu Zhenhua; Lv Zhanmei; Liu Guidong; Efficient numerical methods for hypersingular finite-part integrals with highly oscillatory integrands, Journal of Computational and Applied Mathematics, 2023, 433: 115316. [2] Xu Zhenhua; Lv Zhanmei; Geng Hongrui; Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands, Numerical Algorithms, 2022, 91: 1287-1314. [3] Geng Hongrui; Wang Zhaoran; Xu Zhenhua; Radiation boundary conditions for numerical simulation of transmission problems in acoustics, IAENG International Journal of Applied Mathematics, 2022, 52 (1): 207-212. [4] Hongchao Kang; Chunzhi Xiang; Zhenhua Xu; Hong Wang; Efficient quadrature rules for the singularly oscillatory Bessel transforms and their error analysis, Numerical Algorithms, 2021, 88: 1493–1521. [5] Xu Zhenhua; Geng Hongrui; Fang Chunhua; Asymptotics and numerical approximation of highly oscillatory Hilbert transforms, Applied Mathematics and Computation, 2020, 386: 125525. [6] Xu Zhenhua; Fang Chunhua; Geng Hongrui; Fast computation of Bessel transform with highly oscillatory integrands, Applied Numerical Mathematics, 2019, 145: 121-132. [7] Geng Hongrui; Xu Zhenhua; Coupling of boundary integral equation and finite element methods for transmission problems in acoustics, Numerical Algorithms, 2019, 82: 479–501. [8] Zhenhua Xu; On the Numerical quadrature of weakly singular oscillatory integral and its fast implementation, Taiwanese Journal of Mathematics, 2018, 22:979-1000. [9] Zhenhua Xu; Shuhuang Xiang; Gauss-type quadrature for the highly oscillatory integrals with algebraic singularities and applications, International Journal of Computer Mathematics, 2017, 94(6): 1123-1137. [10] Xu Zhenhua; Milovanovic Gradimir V.; Efficient method for the computation of oscillatory Bessel transform and Bessel Hilbert transform, Journal of Computational and Applied Mathematics, 2016, 308: 117-137. [11] He Guo; Xiang Shuhuang; Xu Zhenhua; A Chebyshev collocation method for a class of Fredholm integral equations with highly oscillatory kernels, Journal of Computational and Applied Mathematics, 2016, 300: 354-368. [12] Xiang Shuhuang; Fang Chunhua; Xu Zhenhua; On uniform approximations to hypersingular finite-part integrals, Journal of Mathematical Analysis and Applications, 2016, 435: 1210-1228. [13] Xu Zhenhua; Xiang Shuhuang; On the evaluation of highly oscillatory finite Hankel transform using special functions, Numerical Algorithms, 2016, 72: 37-56. [14] Xu Zhenhua; Milovanovic Gradimir V.; Xiang Shuhuang; Efficient computation of highly oscillatory integrals with Hankel kernel, Applied Mathematics and Computation, 2015, 261: 312-322. | 