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A fast algorithm for solving the Cauchy problem for ODE using the Sobolev orthogonal polynomials generated by Chebyshev polynomials of the first kind
M. S. Sultanakhmedov, T. N. Shakh-Emirov Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
Abstract:
We consider a numerical implementation of iteration process for solving Cauchy problem for ODE
using the Sobolev orthogonal polynomials generated by Chebyshev polynomials of the first kind $T_0=1/\sqrt{2}$, $T_k(x)=\cos k\arccos x$ ($k\ge1$).
Using the fast DCT, we construct the algorithm for this iteration process and develop the corresponding computer program.
A number of numerical experiments show that the Fourier series by Sobolev – Chebyshev polynomials are very convenient for solving Cauchy problem.
Keywords:
Chebyshev polynomials, Sobolev orthogonal polynomials, fast Fourier transform, discrete cosine transform, fixed-point iteration.
Received: 15.10.2018 Revised: 28.11.2018 Accepted: 29.11.2018
Citation:
M. S. Sultanakhmedov, T. N. Shakh-Emirov, “A fast algorithm for solving the Cauchy problem for ODE using the Sobolev orthogonal polynomials generated by Chebyshev polynomials of the first kind”, Daghestan Electronic Mathematical Reports, 2018, no. 10, 66–76
Linking options:
https://www.mathnet.ru/eng/demr66 https://www.mathnet.ru/eng/demr/y2018/i10/p66
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Abstract page: | 66 | Full-text PDF : | 12 | References: | 6 |
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