Wavelet Collocation Method and Multilevel Augmentation Method for Hammerstein Equations

A wavelet collocation method for nonlinear Hammerstein equations is formulated. A sparsity in the Jacobian matrix is obtained which gives rise to a fast algorithm for nonlinear solvers such as the Newton's method and the quasi-Newton method. A fast multilevel augmentation method is developed on...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2012-01, Vol.34 (1), p.A309-A338
Main Authors: Kaneko, Hideaki, Neamprem, Khomsan, Novaprateep, Boriboon
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Applied mathematics
Approximation
Integral equations
Methods
Nonlinear equations
Sparsity
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Summary:A wavelet collocation method for nonlinear Hammerstein equations is formulated. A sparsity in the Jacobian matrix is obtained which gives rise to a fast algorithm for nonlinear solvers such as the Newton's method and the quasi-Newton method. A fast multilevel augmentation method is developed on a transformed nonlinear equation which gives an additional saving in computational time.
ISSN:1064-8275
1095-7197
DOI:10.1137/100809246