TITLE:
Power and Chebyshev Series Transformation Formulas with Applications to Solving Ordinary Differential Equations via the Fröbenius and Taylor’s Methods
AUTHORS:
Hippolyte Nyengeri, Rénovat Nizigiyimana, Jean-Pierre Mutankana, Henry Bayaga, Ferdinand Bayubahe
KEYWORDS:
Power Series, Chebyshev Polynomials, Economization, Taylor Methods, Fröbenius Method, Ordinary Differential Equations
JOURNAL NAME:
Open Access Library Journal,
Vol.8 No.2,
February
26,
2021
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.