Geodesic
Sparse representation of system of Fredholm integro-differential equations by using Alpert multiwavelets
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1468-1483 
Behzad Nemati Saray; Mehrad Lakestani; Mohsen Razzaghi. Sparse representation of system of Fredholm integro-differential equations by using Alpert multiwavelets. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1468-1483. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a6/
@article{ZVMMF_2015_55_9_a6,
     author = {Behzad Nemati Saray and Mehrad Lakestani and Mohsen Razzaghi},
     title = {Sparse representation of system of {Fredholm} integro-differential equations by using {Alpert} multiwavelets},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1468--1483},
     year = {2015},
     volume = {55},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A numerical technique is presented for the solution of system of Fredholm integro-differential equations. The method consists of expanding the required approximate solution as the elements of Alpert multiwavelet functions (see Alpert B. et al. J. Comput. Phys. 2002, vol. 182, pp. 149–190). Using the operational matrix of integration and wavelet transform matrix, we reduce the problem to a set of algebraic equations. This system is large. We use thresholding to obtain a new sparse system; consequently, GMRES method is used to solve this new system. Numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces accurate results.

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