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Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2017 / Cilt: 13 - Sayı: 1

A Note on Stability Analysis of Taylor Collocation Method

Mehmet SEZER
Sinan DENİZ
Necdet BİLDİK
Pages
149–153
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This equivalence enables us to prove that Taylor collocation method is absolutely stable (A-stable) for the considered equations

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we investigate the stability of Taylor collocation method for initial value problems in ordinary differential equations.
📊
Key Findings & Data:Firstly, we try to show that Taylor collocation method for initial value problem is equivalent to a subset of the implicit Runge-Kutta methods.
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Conclusion & Impact:This equivalence enables us to prove that Taylor collocation method is absolutely stable (A-stable) for the considered equations
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, we investigate the stability of Taylor collocation method for initial value problems in ordinary differential equations. Firstly, we try to show that Taylor collocation method for initial value problem is equivalent to a subset of the implicit Runge-Kutta methods. This equivalence enables us to prove that Taylor collocation method is absolutely stable (A-stable) for the considered equations

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Cite This Article

SEZER, M., DENİZ, S., BİLDİK, N. (2022). A Note on Stability Analysis of Taylor Collocation Method. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 13 - Sayı: 1, 149–153. https://ajindex.com/articles/472308

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References (13)

  1. Bildik, N.; Deniz, S. Implementation of taylor collocation and adomian decomposition method for systems of ordinary differential equations. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014. AIP Publishing. 2015; 1648 (1)
  2. Bildik, N.; Deniz, S. Applications of Taylor collocation method and Lambert W function to systems of delay differential equations. Turk. J. Math. Comput. Sci., Article ID 20130033. 2013; 1-13
  3. Bildik, N.; Deniz, S. Comparative study between Optimal Homotopy Asymptotic Method and PerturbationIteration Technique for different types of nonlinear equations. Iranian Journal of Science and Technology Transactions A: Science. 1-8, (2016); doi: 10.1007/s40995-016-0039- 2
  4. Bildik, N.; Deniz, S. The use of Sumudu Decomposition Method for solving Predator-Prey Systems. Mathematical Sciences Letters.2016; 5(3), 285-289
  5. Deniz, S.; Bildik, N. Optimal Perturbation Iteration Method for Bratu-Type Problems. Journal of King Saud University – Science (2016). (In press)
  6. Karamete, A.; Sezer,M. A Taylor collocation method for the solution of linear integro-differential equations. International Journal of Computer Mathematics. 2002; 79(9), 987-1000
  7. Gülsu, M.; Öztürk,Y.; Sezer,M. A new collocation method for solution of mixed linear integro-differentialdifference equations. Applied Mathematics and Computation. 2010; 216(7), 2183-2198
  8. Bildik, N.; Deniz, S. Comparison of solutions of systems of delay differential equations using Taylor collocation method, Lambert W function and variational iteration method. Scientia Iranica. Transaction D, Computer Science & Engineering and Electrical Engineering. 2015; 22(3), 1052-1058
  9. Deniz, S.; Bildik, N. Comparison of Adomian Decomposition Method and Taylor Matrix Method in Solving Different Kinds of Partial Differential Equations. International Journal of Modeling and Optimization. 2014; 4(4), 292-298
  10. Vasilyev, O.; Bowman, C. Second-generation wavelet collocation method for the solution of partial differential equations. Journal of Computational Physics. 2000; 165 (2), 660-693
  11. Russell-Robert D.; Lawerence, F. A collocation method for boundary value problems. Numerische Mathematik. 1972; 19(1), 1-28
  12. Lanczos, C. Trigonometric interpolation of empirical and analytical functions. Journal of Mathematics and Physics. 1938; 17(1), 123-199
  13. Klaus-Jürgen,B.; Wilson,E. Numerical m