A collocation method using Hermite polynomials for approximate solution of pantograph equations

In this paper, a numerical method based on polynomial approximation, using Hermite polynomial basis, to obtain the approximate solution of generalized pantograph equations with variable coefficients is presented. The technique we have used is an improved collocation method. Some numerical examples, which consist of initial conditions, are given to illustrate the reality and efficiency of the method. In addition, some numerical examples are presented to show the properties of the given method; the present method has been compared with other methods and the results are discussed.

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

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

[3]  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..

[4]  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..

[5]  G. Rao,et al.  Walsh stretch matrices and functional differential equations , 1982 .

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

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

[8]  C. Hwang,et al.  Laguerre series solution of a functional differential equation , 1982 .

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

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

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

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

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

[14]  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.

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

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

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

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

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

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

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