Open Access Library Journal

Volume 8, Issue 2 (February 2021)

ISSN Print: 2333-9705   ISSN Online: 2333-9721

Google-based Impact Factor: 0.60  Citations  

Power and Chebyshev Series Transformation Formulas with Applications to Solving Ordinary Differential Equations via the Fröbenius and Taylor’s Methods

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DOI: 10.4236/oalib.1107142    76 Downloads   290 Views  

ABSTRACT

In this paper, we present formulas that turn finite power series into series of shifted Chebyshev polynomials of the first kind. Thereafter, we derive formulas for coefficients of economized power series obtained by truncating the resulting Chebyshev series. To illustrate the utility of our formulas, we apply them to the solution of first order ordinary differential equations via Taylor methods and to solving the Schr?dinger equation (SE) for a spherically symmetric hyperbolic potential via the Fr?benius method. In each of the two applications, we show that the use of our formulas makes it possible to reduce the computing time, while preserving the accuracy of the results.

Share and Cite:

Nyengeri, H., Nizigiyimana, R., Mutankana, J.-P., Bayaga, H. and Bayubahe, F. (2021) Power and Chebyshev Series Transformation Formulas with Applications to Solving Ordinary Differential Equations via the Fröbenius and Taylor’s Methods. Open Access Library Journal, 8, 1-19. doi: 10.4236/oalib.1107142.

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