Collocation methods for third-kind Volterra integral equations with proportional delays
作者：
Highlights：
• This paper concerns numerical analysis of collocation methods for third-kind Volterra delay integral equations (VDIEs) with noncompact operators.
• The existence, uniqueness and regularity of VDIEs are discussed based on the properties of corresponding Volterra integral operators.
• Collocation methods are applied to VDIEs under two special graded meshes, modified graded mesh and inverted graded mesh, to ensure the solvability of collocation equations.
• The convergence analysis is based on the operator theory. The error bound is estimated by the properties of the Volterra integral operator and its discrete operator.
• Some examples are given to verify the convergence results that the convergence order is m under m collocation parameters.
摘要
•This paper concerns numerical analysis of collocation methods for third-kind Volterra delay integral equations (VDIEs) with noncompact operators.•The existence, uniqueness and regularity of VDIEs are discussed based on the properties of corresponding Volterra integral operators.•Collocation methods are applied to VDIEs under two special graded meshes, modified graded mesh and inverted graded mesh, to ensure the solvability of collocation equations.•The convergence analysis is based on the operator theory. The error bound is estimated by the properties of the Volterra integral operator and its discrete operator.•Some examples are given to verify the convergence results that the convergence order is m under m collocation parameters.
论文关键词：third-kind Volterra integral equations,proportional delays,collocation methods,solvability and convergence,noncompact operators
论文评审过程：Received 9 October 2019, Revised 19 April 2020, Accepted 5 July 2020, Available online 25 July 2020, Version of Record 25 July 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125509
