Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 12, Issue.: 4

Original Research Article

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

 

NUR AMIRAH AHMAD1*, NORAZAK SENU1,2 AND FUDZIAH ISMAIL1,2
1Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.
2Department of Mathematics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

Abstracts

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.