Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators

作者：

Highlights：

• This paper concerns super-convergence of iterated collocation methods for third-kind linear and nonlinear Volterra integral equations (VIEs) with noncompact operators.

• Iterated collocation methods are applied to VIEs under a special modified graded mesh, which improves convergence order in near of singular point t=0.

• By residual function, the iterated error of linear VIEs is estimated based on the operator theory. The global and local super-convergence order are obtained under orthogonal collocation parameters.

• By introducing a transition function, the error function of nonlinear VIEs are transformed into a linear VIEs.

摘要

•This paper concerns super-convergence of iterated collocation methods for third-kind linear and nonlinear Volterra integral equations (VIEs) with noncompact operators.•Iterated collocation methods are applied to VIEs under a special modified graded mesh, which improves convergence order in near of singular point t=0.•By residual function, the iterated error of linear VIEs is estimated based on the operator theory. The global and local super-convergence order are obtained under orthogonal collocation parameters.•By introducing a transition function, the error function of nonlinear VIEs are transformed into a linear VIEs.

论文关键词：Volterra integral equations of third kind,Noncompact operator,Iterated collocation methods,Super-convergence order

论文评审过程：Received 8 December 2020, Revised 12 June 2021, Accepted 25 July 2021, Available online 8 August 2021, Version of Record 8 August 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126562