IJPAM: Volume 107, No. 1 (2016)

NEW EFFICIENT PHASE-FITTED AND
AMPLIFICATION-FITTED RUNGE-KUTTA
METHOD FOR OSCILLATORY PROBLEMS

Firas Adel$^{1,2}$, Norazak Senu$^{1,3}$ Fudziah Ismail$^{1,3}$,
Zanariah Abd. Majid$^{1,3}$
$^{1}$Department of Mathematics
Faculty of Science
Universiti Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA
$^{2}$Department of Mathematics
Faculty of Computer Science and Mathematics
Tikrit University, Sallah AL-Deen, IRAQ
$^3$Institute for Mathematical Research
Universiti Putra Malaysia
43400 UPM, Serdang, Selangor, MALAYSIA


Abstract. A new Runge-Kutta (RK) method is constructed to solve first-order differential equations with oscillatory solutions. This new method is based on the Runge-Kutta method of order four with seven-stage. Numerical tests are performed, and the results of the new method is compared with the existing methods. The numerical results show that the new method is more efficient.

Received: January 4, 2016

AMS Subject Classification: 65L05, 65L06

Key Words and Phrases: Runge-Kutta methods, phase-fitted, amplification-fitted and oscillatory problems

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DOI: 10.12732/ijpam.v107i1.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 1
Pages: 69 - 86


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