Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method
作者：
Highlights：
• Our method is an attractive and easy idea using moving least squares (MLS) and the spectral collocation method to estimate the solution of nonlinear stochastic Volterra integro-differential equations.
• An essential advantage of the proposed technique is that it does not require any preprocessing, such as mesh refinement. Therefore, this method is independent of the geometry of the domains.
• A significant advantage of our approach is that it provided acceptable results with a small number of points and basis functions.
• This method can be used to solve problems with smooth and nonsmoth solution.
摘要
•Our method is an attractive and easy idea using moving least squares (MLS) and the spectral collocation method to estimate the solution of nonlinear stochastic Volterra integro-differential equations.•An essential advantage of the proposed technique is that it does not require any preprocessing, such as mesh refinement. Therefore, this method is independent of the geometry of the domains.•A significant advantage of our approach is that it provided acceptable results with a small number of points and basis functions.•This method can be used to solve problems with smooth and nonsmoth solution.
论文关键词：Stochastic Volterra integro-differential equations,Nonlinear integral equations,Spectral collocation method,Brownian motion process,Moving least squares
论文评审过程：Received 16 December 2020, Revised 24 May 2021, Accepted 6 June 2021, Available online 23 June 2021, Version of Record 23 June 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126447
