A P-STABLE EIGHTEENTH-ORDER SIX-STEP METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

Chunfeng Wang and Zhongcheng Wang
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Chunfeng Wang: Department of Physics, Shanghai University, 99 ShangDa Road, Shanghai 200444, China
Zhongcheng Wang: Department of Physics, Shanghai University, 99 ShangDa Road, Shanghai 200444, China

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 03, 419-431

Abstract: In this paper we present a new kind of P-stable eighteenth-order six-step method for periodic initial-value problems. We add the fourth derivatives to our previous P-stable six-step method to increase the accuracy. We apply two classes of well-known problems to our new method and compare it with the previous methods. The numerical results show that the new method is much more stable, accurate and efficient than the previous methods.

Keywords: Multistep method; P-stable; second-order initial value problem with periodic problems; numerical solution to the Duffing equation; Stiefel and Bettis problem; 02.60.2x; 02.60.Cb; 02.60.Lj; 02.70.2c; 02.70.Bf (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107010449

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