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

Yuzbasi S.

APPLIED MATHEMATICS AND COMPUTATION, cilt.232, ss.1183-1199, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 232
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.amc.2014.01.075
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1183-1199
  • Anahtar Kelimeler: 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 Üniversitesi Adresli: Evet

Özet

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.

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.