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- W3116906776 abstract "In 2016, Sonia et al. first considered the convergence order for the third-kind linear Volterra integral equations (VIEs) based on the assumption that solutions are smooth. For the third-kind linear VIEs with nonsmooth solutions, we construct high-order numerical algorithms and discuss the convergence order. By introducing a new suitable independent variable, we obtain a transformed equation with a smooth exact solution. Then the solvability of the transformed equation is investigated on the basis of piecewise polynomial collocation methods. Meanwhile, the convergence order of the collocation solution is given. Furthermore, based on the inverse transformation, we get the convergence order of the original equation. Numerical simulations are finally presented to demonstrate the effectiveness of the theoretical results." @default.
- W3116906776 created "2021-01-05" @default.
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- W3116906776 date "2020-09-01" @default.
- W3116906776 modified "2023-09-26" @default.
- W3116906776 title "Smoothing transformation and collocation methods for third-kind linear Volterra integral equations" @default.
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- W3116906776 doi "https://doi.org/10.1216/jie.2020.32.361" @default.
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