Revised version of exponentially fitted pseudo-Runge-Kutta method. (4th April 2021)

• Record Type: Journal Article
• Authors: Tiwari, Shruti; Pandey, Ram K.
• Is Part Of: International journal of computing science and mathematics. Volume 13:Number 2(2021)
• Page Start: 116
• Page End: 125
• Publication Date: 2021-04-04
• Subjects: 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; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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 x k 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.