PHASE-FITTED AND AMPLIFICATION-FITTED DIAGONALLY IMPLICIT RUNGE-KUTTA METHOD FOR THE NUMERICAL SOLUTION OF PERIODIC PROBLEMS

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Published: 2016-06-22

Page: 252-264


NUR AMIRAH AHMAD *

Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

NORAZAK SENU

Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. and Department of Mathematics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

FUDZIAH ISMAIL

Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. and Department of Mathematics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

*Author to whom correspondence should be addressed.


Abstract

In this study, we construct a new Phase-fitted and Ampli cation-fitted Diagonally Implicit Runge-Kutta method (PFAFDIRK) for the numerical integration of first order Initial Value Problems (IVPs) which possesses oscillatory solutions. The phase-fitted and amplification-fitted method is based on existing Diagonally Implicit Runge-Kutta method (DIRK) of order four. The numerical results show that the proposed method is more efficient than the existing DIRK methods.

Keywords: Diagonally implicit Runge-Kutta method, ODEs, oscillatory IVPs, phase fitted and amplification fitted


How to Cite

AHMAD, N. A., SENU, N., & ISMAIL, F. (2016). PHASE-FITTED AND AMPLIFICATION-FITTED DIAGONALLY IMPLICIT RUNGE-KUTTA METHOD FOR THE NUMERICAL SOLUTION OF PERIODIC PROBLEMS. Asian Journal of Mathematics and Computer Research, 12(4), 252–264. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/664

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