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 Electronic Mathematical Reports, Tome 10 (2018), pp. 66-76.

Résumé

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.

Détail

Keywords: Chebyshev polynomials, Sobolev orthogonal polynomials, fast Fourier transform, discrete cosine transform, fixed-point iteration.

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