Abstract
In this paper, we consider a linear fuzzy Volterra integral equation of the second kind with a weakly singular kernel which may change sign in the domain of integration. We propose piecewise spline collocation methods with a graded mesh. By increasing the number of collocation points, we show that the numerical solution exists and converges to the exact solution. We obtain exact convergence rates depending on the smoothness of the solution and on the grading parameter of the mesh. We give sufficient conditions for the fuzziness of the approximate solution. The proposed method is illustrated by numerical examples that confirm the theoretical convergence estimates.
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Acknowledgements
The work of Zahra Alijani has been supported by the Estonian Research Council grant PRG864 and ERDF / ESF by the project ’Center for the development of artificial intelligence methods for the automotive industry of the region’ no. CZ.02.1.01 / 0.0 / 17-049 /0008414’. The work of Urve Kangro has been granted by the Estonian Research Council grant PRG864.
Funding
The work of Zahra Alijani has been supported by the Estonian Research Council grant PRG864 and ERDF / ESF by the project ‘Center for the development of artificial intelligence methods for the automotive industry of the region’ no. CZ.02.1.01 / 0.0 / 17-049 /0008414’. The work of Urve Kangro has been granted by the Estonian Research Council grant PRG864.
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Alijani, Z., Kangro, U. Numerical solution of a linear fuzzy Volterra integral equation of the second kind with weakly singular kernels. Soft Comput 26, 12009–12022 (2022). https://doi.org/10.1007/s00500-022-07477-y
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DOI: https://doi.org/10.1007/s00500-022-07477-y