A Bessel collocation method for numerical solution of generalized pantograph equations

This article is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument. In this article, we introduce a collocation method based on the Bessel polynomials for the approximate solution of the pantograph equations. The method is illustrated by studying the initial value problems. The results obtained are compared by the known results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011

[1]  A. Iserles,et al.  Stability of the discretized pantograph differential equation , 1993 .

[2]  Zhanhua Yu.  Variational iteration method for solving the multi-pantograph delay equation , 2008 .

[3]  Alan Feldstein,et al.  THE PHRAGMÉN-LINDELÖF PRINCIPLE AND A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS , 1972 .

[4]  G. Derfel,et al.  On the asymptotics of solutions of a class of linear functional-differential equations , 1996 .

[5]  N. Dyn,et al.  Generalized Refinement Equations and Subdivision Processes , 1995 .

[6]  Mehmet Sezer,et al.  A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument , 2005, Appl. Math. Comput..

[7]  Mehmet Sezer,et al.  A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials , 2005, Int. J. Comput. Math..

[8]  H. I. Freedman,et al.  Analysis of a model representing stage-structured population growth with state-dependent time delay , 1992 .

[9]  Emiko Ishiwata,et al.  On the attainable order of collocation methods for pantograph integro-differential equations , 2003 .

[10]  John Ockendon,et al.  The dynamics of a current collection system for an electric locomotive , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[11]  Mehmet Sezer,et al.  Approximate solution of multi-pantograph equation with variable coefficients , 2008 .

[12]  Mehmet Sezer,et al.  Polynomial solution of high-order linear Fredholm integro-differential equations with constant coefficients , 2008, J. Frankl. Inst..

[13]  Mehmet Sezer,et al.  The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials , 2000, Appl. Math. Comput..

[14]  R. Kanwal,et al.  A Taylor expansion approach for solving integral equations , 1989 .

[15]  Mehmet Sezer,et al.  A Taylor polynomial approach for solving generalized pantograph equations with nonhomogenous term , 2008, Int. J. Comput. Math..

[16]  Mehmet Sezer,et al.  A Taylor method for numerical solution of generalized pantograph equations with linear functional argument , 2007 .

[17]  Mehmet Sezer,et al.  The approximate solution of high-order linear difference equations with variable coefficients in terms of Taylor polynomials , 2005, Appl. Math. Comput..

[18]  Arieh Iserles,et al.  The Pantograph Equation in the Complex Plane , 1997 .

[19]  Mehmet Sezer,et al.  A method for the approximate solution of the second‐order linear differential equations in terms of Taylor polynomials , 1996 .

[20]  M. Z. Liu,et al.  Properties of analytic solution and numerical solution of multi-pantograph equation , 2004, Appl. Math. Comput..

[21]  Mehmet Sezer,et al.  A Taylor polynomial approach for solving differential-difference equations , 2006 .

[22]  Alan Feldstein,et al.  On neutral functional-differential equations with variable time delays , 1998 .

[23]  M. Sezer,et al.  A TAYLOR POLYNOMIAL APPROACH FOR SOLVING HIGH-ORDER LINEAR FREDHOLM INTEGRODIFFERENTIAL EQUATIONS , 2000 .

[24]  L. Fox,et al.  On a Functional Differential Equation , 1971 .

[25]  David J. Evans,et al.  The Adomian decomposition method for solving delay differential equation , 2005, Int. J. Comput. Math..