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    STUDIA MATHEMATICA - Issue no. 2 / 2021  
         
  Article:   A NUMERICAL METHOD FOR TWO-DIMENSIONAL HAMMERSTEIN INTEGRAL EQUATIONS.

Authors:  SANDA MICULA. 		 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2021.2.03

Published Online: 2021-06-15
Published Print: 2021-06-30
pp. 267-277

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In this paper we investigate a collocation method for the approximate solution of Hammerstein integral equations in two dimensions. As in [8], collocation is applied to a reformulation of the equation in a new unknown, thus reducing the computational cost and simplifying the implementation. We start with a special type of piecewise linear interpolation over triangles for a reformulation of the equation. This leads to a numerical integration scheme that can then be extended to any bounded domain in R2, which is used in collocation. We analyze and prove the convergence of the method and give error estimates. As the quadrature formula has a higher degree of precision than expected with linear interpolation, the resulting collocation method is superconvergent, thus requiring fewer iterations for a desired accuracy. We show the applicability of the proposed scheme on numerical examples and discuss future research ideas in this area.

Mathematics Subject Classification (2010): 41A15, 45B05, 47G10, 65D07, 65R20.

Keywords: Hammerstein integral equations, spline collocation, interpolation. 		 
         
     
         
         
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