Approximations to the solution of linear Fredholm integrodifferential-difference equation of high order

Abstract There are few techniques available to numerically solve linear Fredholm integrodifferential-difference equation of high-order. In this paper we show that the Taylor matrix method is a very effective tool in numerically solving such problems. This method transforms the equation and the given conditions into the matrix equations. By merging these results, a new matrix equation which corresponds to a system of linear algebraic equation is obtained. The solution of this system yields the Taylor coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the differential, difference, differential–difference and Fredholm integral equations. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method.

[1]  M. K. Kadalbajoo,et al.  Numerical analysis of singularly perturbed delay differential equations with layer behavior , 2004, Appl. Math. Comput..

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

[3]  Drumi D. Bainov,et al.  Oscillation of the bounded solutions of impulsive differential-difference equations of second order , 2000, Appl. Math. Comput..

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

[5]  T. L. Saaty.  Modern nonlinear equations , 1981 .

[6]  Mehmet Sezer,et al.  A Taylor Collocation Method for the Solution of Linear Integro-Differential Equations , 2002, Int. J. Comput. Math..

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

[8]  M. K. Kadalbajoo,et al.  Numerical Analysis of Boundary-Value Problems for Singularly-Perturbed Differential-Difference Equations with Small Shifts of Mixed Type , 2002 .

[9]  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..

[10]  Zuo Sheng Hu,et al.  Boundedness of solutions to functional integro-differential equations , 1992 .

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

[12]  Jinde Cao,et al.  Delay-dependent robust stability of uncertain nonlinear systems with time delay , 2004, Appl. Math. Comput..