{"title":"Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation","authors":"A. A. El-Sayed","doi":"10.1515/dema-2022-0220","DOIUrl":null,"url":null,"abstract":"Abstract The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders. The studied problem will be transformed into a nonlinear system of algebraic equations. The numerical expansion containing unknown coefficients will be obtained numerically via applying Newton’s iteration method to the claimed system. Convergence analysis and error estimates for the introduced process will be discussed. Numerical applications will be given to illustrate the applicability and accuracy of the proposed method.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Demonstratio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/dema-2022-0220","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders. The studied problem will be transformed into a nonlinear system of algebraic equations. The numerical expansion containing unknown coefficients will be obtained numerically via applying Newton’s iteration method to the claimed system. Convergence analysis and error estimates for the introduced process will be discussed. Numerical applications will be given to illustrate the applicability and accuracy of the proposed method.
期刊介绍：
Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.
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