## Laguerre approach for solving pantograph-type Volterra integro-differential equations

APPLIED MATHEMATICS AND COMPUTATION, vol.232, pp.1183-1199, 2014 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 232
• Publication Date: 2014
• Doi Number: 10.1016/j.amc.2014.01.075
• Journal Name:
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.1183-1199
• Keywords: Pantograph-type Volterra integro-differential equations, Laguerre polynomials, Approximate solutions, Collocation method, Collocation points, Numerical methods, DELAY-DIFFERENTIAL EQUATIONS, NUMERICAL-SOLUTION, RESIDUAL CORRECTION, POLYNOMIAL APPROACH, ERROR ESTIMATION, TAU METHOD, COLLOCATION, STABILITY, ARGUMENTS, DYNAMICS
• Akdeniz University Affiliated: Yes

#### Abstract

In this paper, a collocation method based on Laguerre polynomials is presented to solve the pantograph-type Volterra integro-differential equations under the initial conditions. By using the Laguerre polynomials, the equally spaced collocation points and the matrix operations, the problem is reduced to a system of algebraic equations. By solving this system, we determine the coefficients of the approximate solution of the main problem. Also, an error estimation for the method is introduced by using the residual function. The approximate solution is corrected in terms of the estimated error function. Finally, we give seven examples for the applications of the method on the problem and compare our results by with existing methods.

In this paper, a collocation method based on Laguerre polynomials is presented to solve the pantograph-type Volterra integro-differential equations under the initial conditions. By using the Laguerre polynomials, the equally spaced collocation points and the matrix operations, the problem is reduced to a system of algebraic equations. By solving this system, we determine the coefficients of the approximate solution of the main problem. Also, an error estimation for the method is introduced by using the residual function. The approximate solution is corrected in terms of the estimated error function. Finally, we give seven examples for the applications of the method on the problem and compare our results by with existing methods. (c) 2014 Elsevier Inc. All rights reserved.