Abstract
The classical formula of the barycentric Lagrange interpolation is modified in matrix–vector form and was applied for solving Volterra integral equations. The main aim is to simplify the form of the summation of the classical barycentric formula via matrices to abbreviate the procedure steps so that the round-off error is minimized. Moreover, the barycentric functions are expanded into Taylor polynomials and then represented each polynomial via two matrices; the known coefficient square matrix and the monomial basis matrix. Besides, we substituted the interpolate matrix–vector polynomial for the unknown function into both sides of the integral equation so that an equivalent algebraic system is obtained. The convergence in the mean and the norm of the computational error are given. Two examples are solved. It turns out that the interpolate solutions are obtained equal to the exact solutions for analytic given functions and strongly close to the exact ones for non-analytic functions, which confirms the precision and superiority of the proposed method.
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Shoukralla, E.S., Ahmed, B.M. (2022). Barycentric Lagrange Interpolation Matrix–Vector Form Polynomial for Solving Volterra Integral Equations of the Second Kind. In: Yang, XS., Sherratt, S., Dey, N., Joshi, A. (eds) Proceedings of Sixth International Congress on Information and Communication Technology. Lecture Notes in Networks and Systems, vol 217. Springer, Singapore. https://doi.org/10.1007/978-981-16-2102-4_14
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DOI: https://doi.org/10.1007/978-981-16-2102-4_14
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