Multistep collocation method for Fredholm integral equations of the second kind
作者：
Highlights：
• The multistep collocation method is constructed for Fredholm integral equation with smooth kernels under uniform mesh and weakly singular kernels |s−t|−α(0<α<1) using a graded mesh then the same convergence rate as collocation method but with a lower degree of freedom is obtained.
• In order to avoid the round-off errors caused by graded mesh, a hybrid multistep collocation (HMC) method by combining multistep collocation and hybrid collocation method is proposed. And the detailed convergence analysis has been given.
• The HMC method converges faster with lower degrees of freedom and more efficiently captures the weakly singular properties by nonpolynomial interpolation at the first subinterval.
摘要
•The multistep collocation method is constructed for Fredholm integral equation with smooth kernels under uniform mesh and weakly singular kernels |s−t|−α(0<α<1) using a graded mesh then the same convergence rate as collocation method but with a lower degree of freedom is obtained.•In order to avoid the round-off errors caused by graded mesh, a hybrid multistep collocation (HMC) method by combining multistep collocation and hybrid collocation method is proposed. And the detailed convergence analysis has been given.•The HMC method converges faster with lower degrees of freedom and more efficiently captures the weakly singular properties by nonpolynomial interpolation at the first subinterval.
论文关键词：Fredholm integral equations,Multistep collocation,Hybrid multistep collocation,Weakly singular kernels,Fast algorithm
论文评审过程：Received 5 September 2021, Revised 8 December 2021, Accepted 11 December 2021, Available online 31 December 2021, Version of Record 31 December 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126870
