• 论文 • 上一篇    

弱奇异时滞Volterra积分方程雅可比收敛分析

郑伟珊   

  1. 韩山师范学院数学与统计学院, 潮州 521041
  • 收稿日期:2020-01-22 发布日期:2021-05-13
  • 基金资助:
    国家自然科学基金项目(11626074)、广东省自然科学基金项目(2017A030307020)和韩山师范学院项目(HJG1629、2017HJGJCJY009)资助.

郑伟珊. 弱奇异时滞Volterra积分方程雅可比收敛分析[J]. 计算数学, 2021, 43(2): 253-260.

Zheng Weishan. JACOBI CONVERGENCE ANALYSIS FOR DELAY VOLTERRA INTEGRAL EQUATION WITH WEAK SINGULARITY[J]. Mathematica Numerica Sinica, 2021, 43(2): 253-260.

JACOBI CONVERGENCE ANALYSIS FOR DELAY VOLTERRA INTEGRAL EQUATION WITH WEAK SINGULARITY

Zheng Weishan   

  1. College of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China
  • Received:2020-01-22 Published:2021-05-13
本文利用雅可比谱配置方法研究弱奇异时滞Volterra积分方程,分别得到真解与近似解在$L^{\infty}$和$L^2_{\omega^{-\mu,0}}$ 范数意义下呈现指数收敛的结论,数值仿真结果验证理论分析的正确性.
In this paper, Jacobi spectral method is employed to analysis the convergence of weak singular Volterra integral equation with delay. The conclusion is that the numerical error decay exponentially in the $L^{\infty}$ space and $L^2_{\omega^{-\mu,0}}$ space. In the end, numerical examples are given to confirm the theoretical result.

MR(2010)主题分类: 

()
[1] Wang S, Xie X. The Volterra's integral equation theory for accelerator single-freedom nonlinear components[J]. Chinese J. Nucl. Phy., 1996, 18(2):118-124.
[2] Kang L, Wang S, Jiang T B. Hydrologic model of Volterra neural network and its application[J]. J. Hydr. Eng., 2006, 25(5):22-26.
[3] Zhang C H, Yan X P. Positive solution bifurcating from zero solution in a Lotka-Volterra competitive system with cross-diffusion effects[J]. Appl. Math. J. Chinese Univ., 2011, 25(3):342-352.
[4] Tang T, Xu X, Cheng J. On spectral methods for Volterra integral equations and the convergence analysis[J]. J. Comput. Math., 2008, 26:825-837.
[5] Chen Y P, Tang T. Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel[J]. Math. Comput., 2010, 79(269):147-167.
[6] Xie Z, Li X, Tang T. Convergence analysis of spectral Galerkin methods for Volterra type integral equations[J]. J. Sci. Comput., 2012, 53:414-434.
[7] Wei Y X, Chen Y P. Convergence analysis of the spectral methods for weakly singular Volterra integro-differential equations with smooth solutions[J]. Adv. Appl. Math. Mech., 2012, 4(1):1-20.
[8] Chen Y P, Li X J, Tang T. A note on Jacobi spectral-collocation methods for weakly singular Volterra integral equations with smooth solutions, J. Comput. Math., 2013, 31(1):47-56.
[9] Yong J M. Backward stochastic Volterra integral equations-a brief survey[J]. Appl. Math. J. Chinese Univ., 2013, 28(4):383-394.
[10] Zheng W S, Chen Y P. A spectral method for second order Volterra integro-differential equations with pantograph delay[J]. Adv. Appl. Math. Mech., 2013, 5(2):131-145.
[11] Yang Y, Chen Y P, Huang Y Q. Convergence analysis of Legendre-collocation methods for nonlinear Volterra type integro equations[J]. Adv. Appl. Math. Mech., 2015, 7:74-88.
[12] Dahaghin M Sh, Eskandari Sh. Solving two-dimensional Volterra-Fredholm integral equations of the second kind by using Bernstein polynomials[J]. Appl. Math. J. Chinese Univ., 2017, 32(1):68-78.
[13] Zheng W S, Chen Y P. Numerical analysis for Volterra integral equation with two kinds of delay[J]. Acta Math. Sci., 2019, 39(2):607-617.
[14] Zheng W S, Chen Y P, Huang Y Q. Convergence Analysis of Legendre-collocation spectral methods for second order Volterra integro-differential equation with delay. Adv. Appl. Math. Mech., 2019, 11(2):486-500.
[15] Henry D. Geometric theory of semilinear parabolic equations[M]. Springer-Verlag, Heidelberg, 1989.
[16] Canuto C, Hussaini M Y, Quarteroni A, et al. Spectral methods fundamentals in single domains[M]. Springer-Verlag, Heidelberg, 2006.
[17] Mastroianni G, Occorsio D. Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey[J]. J. Comput. Appl. Math., 2001, 134:325-341.
[18] Ragozin D L. Polynomial approximation on compact manifolds and homogeneous spaces[J]. Trans. Amer. Math. Soc., 1970, 150:41-53.
[19] Ragozin D L. Constructive polynomial approximation on spheres and projective spaces[J]. Trans. Amer. Math. Soc., 1971, 162:157-170.
[20] Kufner A, Persson L E. Weighted Inequalities of Hardy Type[M]. World Scientific, New York, 2003.
[21] Nevai P. Mean convergence of Lagrange interpolation:III[J]. J. Comput. Appl. Math., 1991, 34:385-396.
[1] 古振东, 孙丽英. 非线性第二类Volterra积分方程的Chebyshev谱配置法[J]. 计算数学, 2020, 42(4): 445-456.
[2] 丛玉豪, 胡洋, 王艳沛. 含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性[J]. 计算数学, 2019, 41(1): 104-112.
[3] 彭新俊, 王翼飞. 模拟化学反应系统的快速无偏τ-Leap算法[J]. 计算数学, 2009, 31(3): 309-322.
[4] 张志平,. 时滞偏害系统的稳定性和分歧分析[J]. 计算数学, 2008, 30(2): 213-224.
[5] 甘四清,孙耿. Runge-Kutta方法关于时滞奇异摄动问题的误差分析[J]. 计算数学, 2001, 23(3): 343-356.
阅读次数
全文


摘要