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 - <p style="text-align: justify;">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.</p>