Geodesic
A new sequential approach for solving the integro-differential equation via Haar wavelet bases
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2 
H. Beiglo; M. Erfanian; M. Gachpazan. A new sequential approach for solving the integro-differential equation via Haar wavelet bases. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a6/
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     author = {H. Beiglo and M. Erfanian and M. Gachpazan},
     title = {A new sequential approach for solving the integro-differential equation via {Haar} wavelet bases},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {302},
     year = {2017},
     volume = {57},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this work, we present a method for numerical approximation of fixed point operator, particularly for the mixed Volterra–Fredholm integro-differential equations. The main tool for error analysis is the Banach fixed point theorem. The advantage of this method is that it does not use numerical integration, we use the properties of rationalized Haar wavelets for approximate of integral. The cost of our algorithm increases accuracy and reduces the calculation, considerably. Some examples are provided toillustrate its high accuracy and numerical results are compared with other methods in the other papers.

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