Numerical solution for the weakly singular Fredholm integro-differential equations using Legendre multiwavelets

Lakestanı M., Saray B. N., Dehghan M.

Journal of Computational and Applied Mathematics, cilt.235, sa.11, ss.3291-3303, 2011 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 235 Sayı: 11
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.cam.2011.01.043
  • Dergi Adı: Journal of Computational and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3291-3303
  • Anahtar Kelimeler: Legendre multiwavelets, Operational matrix of integral, Sparse matrix, Spectral method, Thresholding, Weakly singular integro-differential equation
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

An effective method based upon Legendre multiwavelets is proposed for the solution of Fredholm weakly singular integro-differential equations. The properties of Legendre multiwavelets are first given and their operational matrices of integral are constructed. These wavelets are utilized to reduce the solution of the given integro-differential equation to the solution of a sparse linear system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain the solution to this system of algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of the resulted matrix equation. © 2011 Elsevier B.V. All rights reserved.