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<p>We consider the numerical solution of nonlinear Fredholm integral equations of the second kind. The problem is solved by combining fixed-point iterations with a collocation method using Chebyshev polynomial bases. The kernel is approximated by a truncated Chebyshev series, and collocation at Chebyshev roots yields the unknown coefficients via discrete orthogonality. The solution is obtained by Chebyshev interpolation. An error estimate is obtained in the Banach space of measurable functions. Numerical results confirm the effectiveness of the approach.</p>

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CONSTRUCTION OF SOLUTIONS TO NONLINEAR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

  • 期刊论文

  • 发表日期：

    2026年6月24日

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  • Oksana Germider,
  • Vasilii Popov

摘要

We consider the numerical solution of nonlinear Fredholm integral equations of the second kind. The problem is solved by combining fixed-point iterations with a collocation method using Chebyshev polynomial bases. The kernel is approximated by a truncated Chebyshev series, and collocation at Chebyshev roots yields the unknown coefficients via discrete orthogonality. The solution is obtained by Chebyshev interpolation. An error estimate is obtained in the Banach space of measurable functions. Numerical results confirm the effectiveness of the approach.