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On the collocation method for constructing a solution to the nonlinear Fredholm integral equation of the second kind using Chebyshev polynomials
| Title | On the collocation method for constructing a solution to the nonlinear Fredholm integral equation of the second kind using Chebyshev polynomials |
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| Authors | V. N. Popov1, O. V. Germider1 1Northern (Arctic) Federal University named after M.V. Lomonosov |
| Annotation | Using the method of successive approximations and properties of systems of orthogonal Chebyshev polynomials of the first kind, a matrix implementation of the collocation method for constructing solutions of nonlinear Fredholm integral equations of the second kind is proposed. The integral function in the equations under consideration is represented as a partial sum of a series over these polynomials. The roots of Chebyshev polynomials are chosen as collocation points. The desired solutions are found by polynomial interpolation of the obtained function values at the collocation points using the properties of inverse matrices, the elements of which are written based on orthogonal relations for these polynomials. |
| Keywords | collocation method, sequential approximation method, Chebyshev polyno- mials, integral equations. |
| Citation | Popov V. N., Germider O. V. ''On the collocation method for constructing a solution to the nonlinear Fredholm integral equation of the second kind using Chebyshev polynomials'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 163-166. Available at: https://conf.svmo.ru/files/2024/papers/paper29.pdf. - Date of access: 16.10.2024. |
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