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Nyengeri, H., Manariyo, B., Nizigiyimana, R. and Mugisha, S. (2020) Application of the Economization of Power Series to Solving The Schrödinger Equation for the Gaussian Potential via the Asymptotic Iteration Method. Open Access Library Journal, 7, e6505.
https://dx.doi.org/10.4236/oalib.1106505

has been cited by the following article:

• 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.