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A numerical technique for solving Volterra-Fredholm integral equations using Chebyshev spectral method

Abstract

In this study, we propose a highly accurate technique for solving Volterra and Fredholm integral equations based on the blending of the Chebyshev pseudo methods. The application of the method leads Volterra and Fredholm integral equation to a system of linear algebraic equations that are easy to solve when compared to a integral equations. Some examples are solved and presented through graphs and tables and the obtained results are compared with those methods in the literature to illustrate the ability of the method. The results demonstrate that the new method is more efficient, converges and accurate to the exact solution.

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Correspondence to Ahmed A. Khidir.

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Khidir, A.A. A numerical technique for solving Volterra-Fredholm integral equations using Chebyshev spectral method. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00692-7

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  • DOI: https://doi.org/10.1007/s11587-022-00692-7

Keywords

  • Volterra-Fredholm integral equations
  • Chebyshev collocation method
  • Successive linearization method