SavedAdd your journal

Journals / New Trends in Mathematical Sciences / 2015 / Cilt: 3 Sayı: 2

Bernoulli collocation method for high-order generalized pantograph equations

Ayşegül Daşçıoğlu
Mehmet Sezer
Pages
96–109
Publication Date
2015-01-19
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Some numerical examples have beengiven to illustrate the reliability and efficiency of the method

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, an approximate method based on Bernoulli polynomials has been presented to obtain the solution ofgeneralized pantograph equations with linear functional arguments.
📊
Key Findings & Data:Both initial and boundary value problems have been solved by thiscollocation technique.
💡
Conclusion & Impact:Some numerical examples have beengiven to illustrate the reliability and efficiency of the method
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Pantograph equations · Functional differential equations · Bernoulli polynomials

Abstract

In this paper, an approximate method based on Bernoulli polynomials has been presented to obtain the solution ofgeneralized pantograph equations with linear functional arguments. Both initial and boundary value problems have been solved by thiscollocation technique. Approximate solution can also be corrected with the residual function. Some numerical examples have beengiven to illustrate the reliability and efficiency of the method

🔖

Cite This Article

Daşçıoğlu, A., Sezer, M. (2015). Bernoulli collocation method for high-order generalized pantograph equations. New Trends in Mathematical Sciences, Cilt: 3 Sayı: 2, 96–109. https://ajindex.com/articles/1003887

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (13)

  1. J.R. Ockendon, A.B. Tayler, The dynamics of a current collection system for an electric locomotive, Proc. Roy. Soc. London, Ser. A 322 (1971) 447-468.
  2. L. Fox, D.F. Mayers, J.A. Ockendon, A.B. Tayler, On a functional differential equation, J. Inst. Math. Appl. 8 (1971) 271-307.
  3. W.G. Ajello, H.I. Freedman, J.Wu, A model of stage structured population growth with density depended time delay, SIAM J. Appl. Math. 52 (1992) 855-869.
  4. M.D. Buhmann, A. Iserles, Stability of the discretized pantograph differential equation, Math. Comput. 60 (1993) 575-589.
  5. G.R. Morris, A. Feldstein, E.W. Bowen, The Phragmen-Lindel’ of principle and a class of functional-differential equations, in: Proceedings of NRL-MRC Conference on Ordinary Differential Equations, 1972, pp. 513-540.
  6. G. Derfel, On compactly supported solutions of a class of functional-differential equations, in: Modern Problems of Functions Theory and Functional Analysis, Karaganda University Press. 1980 (in Russian). G. Derfel, N. Dyn, D. Levin, Generalized refinement equation and subdivision process, J. Approx. Theory 80 (1995) 272-297.
  7. G.A. Derfel, F. Vogl, On the asymptotic of solutions of a class of linear functional-differential equations, European J. Appl. Maths. 7 (1996) 511-518.
  8. G. Derfel, A.Iserles, The pantograph equation in the complex plane, J. Math. Anal. Appl. 213 (1997) 117-132.
  9. A. Feldstein, Y. Liu, On neutral functional-differential equations with variable time delays, Math. Proc. Cambridge Philos. Soc. 124 (1998) 371-384.
  10. M.Z. Liu, D. Li, Properties of analytic solution and numerical solution and multi-pantograph equation, Appl. Math. Comput. 155 (2004) 853-871. M. G¨ulsu, M. Sezer, The approximate solution of high-order linear difference equation with variable coefficients in terms of Taylor polynomials, Appl. Math. Comput. 168 (1) (2005) 76-88.
  11. M. Sezer, M. G¨ulsu, A new polynomial approach for solving difference and Fredholm integro-difference equation with mixed argument, Appl. Math. Comput. 171 (1) (2005) 332-344. M. G¨ulsu, M. Sezer, A Taylor polynomial approach for solving differential-difference equations, J. Comput. Appl. Math. 186 (2) (2006) 349-364.
  12. M. Sezer, A. Aky¨uz-Das¸cıo˘glu, Taylor polynomial solutions of general linear differential–difference equations with variable coefficients, Appl. Math. Comput. 174 (2006) 1526–1538.
  13. M. Sezer, S. Yalc¸ınbas¸, N. S¸ahin, Approximate solution of multi-pantograph equation with variable coefficients, J. Comput. Appl. Math. 214 (2008) 406-416. M