Title: Revised version of exponentially fitted pseudo-Runge-Kutta method
Authors: Shruti Tiwari; Ram K. Pandey
Addresses: Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, Sagar (M.P.), India ' Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, Sagar (M.P.), India
Abstract: In this paper, we have proposed the revised version of exponentially-fitted (ef) pseudo-Runge-Kutta method (ef-PRKM). The motivation behind the revision is to fill the leakage of error in the internal stages during the fitting process. Generally, the internal stage operator, in an ef-PRKM or ef-Runge-Kutta method (ef-RKM) integrates two exponential functions exp(± ωx), with unknown frequency ω ε R (for trigonometric-fitting exp(± ωx), ω ε iR). However, these internal stage operators produce some amount of errors in integrating other functions like xk exp(± ωx), k ≥ 0 . Here, we first measure the error expression and taking into account this error, we redefine the external stage (solution) operators and compute the revised weights of the ef-PRKM. The revised ef-PRKM is tested on two initial value problems (IVPs). The results are reported in tables and figure. The proposed method would be a good option to find the numerical solution of IVPs efficiently with less cost consumption in the form of slopes/function evaluations than the standard Runge-Kutta methods.
Keywords: pseudo-Runge-Kutta Method; exponential fitting; local truncation error; numerical solution of IVP; IVP; initial value problem; oscillatory solution; cost of computation; function evaluations; relative error; stage operator.
International Journal of Computing Science and Mathematics, 2021 Vol.13 No.2, pp.116 - 125
Received: 07 Oct 2019
Accepted: 14 Jun 2020
Published online: 13 Apr 2021 *