TY - JOUR
T1 - Spectral Scheme for Nonlinear Volterra Integro-Differential Equation
AU - Zheng , Weishan
AU - Chen , Yanping
AU - Zhou , Jianwei
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1395
EP - 1410
PY - 2025
DA - 2025/07
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2022-0164
UR - https://global-sci.org/intro/article_detail/aamm/24285.html
KW - Legendre spectral method, nonlinear Volterra integro-differential equation, numerical simulation.
AB - <p style="text-align: justify;">Nonlinear problems widely exist in many aspects of the natural field. The
nonlinear situation makes it difficult for most existing solvers to deal with. Therefore, constructing an efficient and accurate solver is a challenge. In this paper, a Legendre
spectral method is developed for the nonlinear Volterra integro-differential equation.
The error analysis is also provided to justify the spectral rate of convergence for the errors of approximate solution and approximate derivative decay exponentially in both
the $L^2$ norm and the infinity norm. In the end, numerical results are displayed to confirm the effectiveness of the Legendre spectral analysis.</p>