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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
It is proven that under particular choices of the auxiliary parameters the homotopy perturbation method is indeed the Taylor series expansion of the sought solution of nonlinear equations.
📌 3 Key Takeaways
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Objective & Hypothesis:The present paper deals with the homotopy perturbation method.
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Key Findings & Data:The question of whether the homotopy perturbation method is simply the conventional Taylor series expansion is examined.
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Conclusion & Impact:It is proven that under particular choices of the auxiliary parameters the homotopy perturbation method is indeed the Taylor series expansion of the sought solution of nonlinear equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Nonlinearity · Analytic solution · Homotopy perturbation method
Abstract
The present paper deals with the homotopy perturbation method. The question of whether the homotopy perturbation method is simply the conventional Taylor series expansion is examined. It is proven that under particular choices of the auxiliary parameters the homotopy perturbation method is indeed the Taylor series expansion of the sought solution of nonlinear equations.
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Cite This Article
Turkyilmazoglu, M. (2015). Is homotopy perturbation method the traditional Taylor series expansion. Hacettepe Journal of Mathematics and Statistics, Volume: 44 Issue: 3. https://ajindex.com/articles/1403288