An explicit six-step singularly P-stable Obrechkoff method for the numerical solution of second-order oscillatory initial value problems
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In this paper, we present an explicit six-step singularly P-stable Obrechkoff method of tenth algebraic order for solving second-order linear periodic and oscillatory initial value problems of ordinary differential equations. The advantage of this new singularly P-stable Obrechkoff method is that it is a high-order explicit method, and thus does not require additional predictor stages. The numerical stability and phase properties of the new method is analyzed. Four numerical examples show that the new explicit method is more accurate than Obrechkoff schemes of the same order when applied to the numerical solution of second-order initial value problems with highly oscillatory solutions.
KeywordsExplicit methods Phase-lag Ordinary differential equations Singularly P-stable Symmetric multistep methods
Mathematics Subject Classification (2010)Primary: 65L05 Secondary: 65L06
The authors wish to thank the anonymous referees for their careful reading of the manuscript and their fruitful comments and suggestions which improved the presentation of this paper.
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