A HIGHLY ACCURATE AND EFFICIENT TRIGONOMETRICALLY-FITTED P-STABLE THREE-STEP METHOD FOR PERIODIC INITIAL-VALUE PROBLEMS

Zhongcheng Wang, Yongming Dai and Dongmei Wu
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Zhongcheng Wang: Department of Physics, Shanghai University, 99 Shang Da Road, Shanghai 200444, P. R. China
Yongming Dai: Department of Physics, Shanghai University, 99 Shang Da Road, Shanghai 200444, P. R. China
Dongmei Wu: Department of Physics, Shanghai University, 99 Shang Da Road, Shanghai 200444, P. R. China

International Journal of Modern Physics C (IJMPC), 2006, vol. 17, issue 04, 545-560

Abstract: In this paper we present a new three-step method, which is a trigonometrically-fitted P-stable Obrechkoff method with phase-lag (frequency distortion) infinity. In this new method, we make use of higher-even-order derivatives including the eighth-order to increase the accuracy. On the other hand, we adopt a special structure to reduce the computational complexity of high-derivatives. The numerical illustration demonstrate that the new method has advantage in accuracy, periodic stability and efficiency.

Keywords: Obrechkoff method; high-order derivative; first-order derivative formula; second-order initial value problem with periodic solutions; numerical solution to the Duffing equation; 02.60.2x; 02.60.Cb; 02.60.Lj; 02.70.2c; 02.70.Bf (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0129183106008674

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