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Volume 48, Issue 4
Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels

Jie Shen, Changtao Sheng & Zhongqing Wang

DOI: 10.4208/jms.v48n4.15.01

J. Math. Study, 48 (2015), pp. 315-329.

Published online: 2015-12

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  • Abstract

We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations (VIEs) with weakly singular kernels. We establish the existence and uniqueness of the numerical solution, and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity. We also present numerical results which are consistent with the theoretical predictions.

  • Keywords

Generalized Jacobi spectral-Galerkin method, nonlinear Volterra integral equations with weakly singular kernels, convergence analysis.

  • AMS Subject Headings

45D05, 65L60, 41A30, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

shen7@purdue.edu (Jie Shen)

ctsheng@stu.xmu.edu.cn (Changtao Sheng)

zqwang@usst.edu.cn (Zhongqing Wang)

  • BibTex
  • RIS
  • TXT
@Article{JMS-48-315, author = {Shen , JieSheng , Changtao and Wang , Zhongqing}, title = {Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {4}, pages = {315--329}, abstract = {

We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations (VIEs) with weakly singular kernels. We establish the existence and uniqueness of the numerical solution, and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity. We also present numerical results which are consistent with the theoretical predictions.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n4.15.01}, url = {http://global-sci.org/intro/article_detail/jms/9936.html} }
TY - JOUR T1 - Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels AU - Shen , Jie AU - Sheng , Changtao AU - Wang , Zhongqing JO - Journal of Mathematical Study VL - 4 SP - 315 EP - 329 PY - 2015 DA - 2015/12 SN - 48 DO - http://doi.org/10.4208/jms.v48n4.15.01 UR - https://global-sci.org/intro/article_detail/jms/9936.html KW - Generalized Jacobi spectral-Galerkin method, nonlinear Volterra integral equations with weakly singular kernels, convergence analysis. AB -

We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations (VIEs) with weakly singular kernels. We establish the existence and uniqueness of the numerical solution, and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity. We also present numerical results which are consistent with the theoretical predictions.

Shen , JieSheng , Changtao and Wang , Zhongqing. (2015). Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels. Journal of Mathematical Study. 48 (4). 315-329. doi:10.4208/jms.v48n4.15.01
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