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On a numerical method based on wavelets for Fredholm‐Hammerstein integral equations of the second kind
Author(s) -
Micula Sanda,
Cattani Carlo
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4952
Subject(s) - mathematics , collocation method , collocation (remote sensing) , convergence (economics) , fredholm integral equation , integral equation , nonlinear system , wavelet , fredholm theory , mathematical analysis , computer science , differential equation , ordinary differential equation , artificial intelligence , physics , quantum mechanics , machine learning , economic growth , economics
In this paper, we consider a special kind of nonlinear integral equations, Fredholm‐Hammerstein equations. As done before we use an equivalent reformulation, for which collocation methods are more efficient. For the alternative equation, we use a collocation method based on Haar wavelets to approximate the solution. We discuss the convergence and error analysis of the method, showing that, at the collocation nodes, the order of convergence is higher than expected. The paper concludes with numerical examples, which illustrate the good approximations, conclusions, and ideas for future work in this area.