Numerical results withcomparisons are given to confirm the reliability of the proposed method forsolving generalized pantograph equations with variable coefficients.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we present an efficient direct solver for solvingthe generalizedpantograph equations with variable coefficients.
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Key Findings & Data:An approachis based on thesecond kind Chebyshev polynomials together with operational method.
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Conclusion & Impact:Numerical results withcomparisons are given to confirm the reliability of the proposed method forsolving generalized pantograph equations with variable coefficients.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we present an efficient direct solver for solvingthe generalizedpantograph equations with variable coefficients. An approachis based on thesecond kind Chebyshev polynomials together with operational method. Themain characteristic behind this approach is that it reducessuch problem to onesof solving systems of algebraic equations. Only a small number ofChebyshevpolynomials are needed to obtain a satisfactory result. Numerical results withcomparisons are given to confirm the reliability of the proposed method forsolving generalized pantograph equations with variable coefficients.
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Cite This Article
GÜLSU, M., ÖZTÜRK, Y. (2022). Approximate solution of generalized pantograph equations withvariable coefficients by operational method. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 7 - Sayı: 1, 66–74. https://ajindex.com/articles/440675
Ockendon, J.R. and Tayler, A.B., The dynamics of a current collection system for an electric lo- comotive. Proc. Roy. Soc. London, Ser. A, 322, 447-468 (1971).
Ajello, W.G., Freedman, H.I. and Wu, J., Analy- sis of a model representing stage-structured pop- ulation growth with state-dependent time delay. SIAM J. Appl. Math., 52, 855-869 (1992).
Buhmann, M.D. and Iserles, A., Stability of the discretized pantograph differential equation. Math. Comput., 60, 575-589 (1993).
Derfel, G., On compactly supported solutions of a class of functional-differential equations, in Modern Problems of Function Theory and Functional Analysis. Karaganda University Press, Kazakhstan, (1980).
Feldstein, A. and Liu, Y., On neutral functional- differential equations with variable time delays. Math. Proc. Camb. Phil. Soc., 124, 371-384 (1998).
Derfeland, G. and Levin, D., Generalized refine- ment equation and subdivision process. J. Approx. Theory, 80, 272-297 (1995).
Sezer, M. and Akyuz, A., A Taylor method for nu- merical solution of generalized pantograph equa- tion with linear functional argument. J. Comp. Appl. Math., 200, 217-225 (2007).
Sezer, M., Yalnbas, S. and Sahin, N., Approxi- mate solution of multi-pantograph equation with variable coefficients. J. Comp. Appl. Math., 214, 406-416 (2008).
Saadatmandi, A. and Dehghan, M., Variational iteration method for solving a generalized pantgo- raph equation. Comp. Math. Appl., 58, 2190-2196 (2009).
Evans, D.J. and Raslan, K.R., The Adomian de- composition method for solving delay differen- tial equation. Int. J. Comp. Math., 82(1), 49-54 (2005).
Buhmann, M. and Iserles, A., Stability of the discretized pantograph differential equation. J. Math. Comp., 60, 575-589 (2005).
Li, D. and Liu, M.Z., Runge-Kutta methods for the multi-pantograph delay equation. Appl. Math. Comp., 163, 383-395 (2005).
Shakeri, F. and Dehghan, M., Solution of the de- lay differential equations via homotopy perturba- tion method. Math. Comp. Modelling, 48, 486-498 (2008).
Muroya, Y., Ishiwata, E. and Brunner, E., On the attainable order of collocation methods for pan- tograph integro-differential equations. J. Comp. Appl. Math., 152, 347-366 (2003).
Huan-Yu, Z., Variational iteration method for solving the multi-pantograph delay equation. Physics Letter A, 372 (43), 6475-6479 (2008).
Sezer, M. and Gulsu, M., A new polynomial approach for solving difference and Fredho