This paper considers Volterra integral equations (VIEs) of the third kind. We present a novel multi-interval collocation-based approach for the numerical solution of this type of equations. The proposed method is particularly effective for VIEs when implemented in continuous piecewise polynomial spaces, leveraging its ability to perform localized approximations on subintervals. We also analyze the solvability of the proposed continuous collocation schemes and establish its convergence properties. Numerical experiments are included to demonstrate the spectral accuracy of the method and validate the theoretical findings.
Davari, A. (2025). A multi-interval continuous collocation method for Volterra integral equations of the third kind. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.67851.3244
MLA
Davari, A. . "A multi-interval continuous collocation method for Volterra integral equations of the third kind", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.67851.3244
HARVARD
Davari, A. (2025). 'A multi-interval continuous collocation method for Volterra integral equations of the third kind', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.67851.3244
CHICAGO
A. Davari, "A multi-interval continuous collocation method for Volterra integral equations of the third kind," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.67851.3244
VANCOUVER
Davari, A. A multi-interval continuous collocation method for Volterra integral equations of the third kind. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.67851.3244
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