Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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LEGENDRE EXPANSION METHODS FOR THE NUMERICAL SOLUTION OF NONLINEAR 2D FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

  • Nemati, S. (Department of Mathematics and Computer Science, University of Mazandaran) ;
  • Ordokhani, Y. (Department of Mathematics, Alzahra University)
  • Received : 2012.07.04
  • Accepted : 2013.03.16
  • Published : 2013.09.30
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Abstract

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

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References

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