Volume 38, Issue 4
Implicity Linear Collocation Method and Iterated Implicity Linear Collocation Method for the Numerical Solution of Hammerstein Fredholm Integral Equations on 2D Irregular Domains

H. Laeli Dastjerdi & M. Nili Ahmadabadi

J. Comp. Math., 38 (2020), pp. 624-637.

Published online: 2020-04

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  • Abstract

In this work, we adapt and compare implicity linear collocation method and iterated implicity linear collocation method for solving nonlinear two dimensional Fredholm integral equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain. IMQs show to be the most promising RBFs for this kind of equations. The proposed methods are mesh-free and they are independent of the geometry of domain. Convergence analysis of the proposed methods together with some benchmark examples are provided which support their reliability and numerical stability.

  • Keywords

Two dimensional equations, Irregular domain, Fredholm integral equations, Mesh-less method, Numerical treatment.

  • AMS Subject Headings

45G10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hojatld@gmail.com (H. Laeli Dastjerdi)

mneely59@hotmail.com (M. Nili Ahmadabadi)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-624, author = {Laeli Dastjerdi , H. and Ahmadabadi , M. Nili }, title = {Implicity Linear Collocation Method and Iterated Implicity Linear Collocation Method for the Numerical Solution of Hammerstein Fredholm Integral Equations on 2D Irregular Domains}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {4}, pages = {624--637}, abstract = {

In this work, we adapt and compare implicity linear collocation method and iterated implicity linear collocation method for solving nonlinear two dimensional Fredholm integral equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain. IMQs show to be the most promising RBFs for this kind of equations. The proposed methods are mesh-free and they are independent of the geometry of domain. Convergence analysis of the proposed methods together with some benchmark examples are provided which support their reliability and numerical stability.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1903-m2017-0206}, url = {http://global-sci.org/intro/article_detail/jcm/16466.html} }
TY - JOUR T1 - Implicity Linear Collocation Method and Iterated Implicity Linear Collocation Method for the Numerical Solution of Hammerstein Fredholm Integral Equations on 2D Irregular Domains AU - Laeli Dastjerdi , H. AU - Ahmadabadi , M. Nili JO - Journal of Computational Mathematics VL - 4 SP - 624 EP - 637 PY - 2020 DA - 2020/04 SN - 38 DO - http://doi.org/10.4208/jcm.1903-m2017-0206 UR - https://global-sci.org/intro/article_detail/jcm/16466.html KW - Two dimensional equations, Irregular domain, Fredholm integral equations, Mesh-less method, Numerical treatment. AB -

In this work, we adapt and compare implicity linear collocation method and iterated implicity linear collocation method for solving nonlinear two dimensional Fredholm integral equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain. IMQs show to be the most promising RBFs for this kind of equations. The proposed methods are mesh-free and they are independent of the geometry of domain. Convergence analysis of the proposed methods together with some benchmark examples are provided which support their reliability and numerical stability.

H. Laeli Dastjerdi & M. Nili Ahmadabadi. (2020). Implicity Linear Collocation Method and Iterated Implicity Linear Collocation Method for the Numerical Solution of Hammerstein Fredholm Integral Equations on 2D Irregular Domains. Journal of Computational Mathematics. 38 (4). 624-637. doi:10.4208/jcm.1903-m2017-0206
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