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On the existence and the approximation of solutions of Volterra integral equations of the second kind

Author

Listed:
  • Ezquerro, J.A.
  • Hernández-Verón, M.A.
  • Magreñán, Á.A.
  • Moysi, A.

Abstract

We study the existence of solution of Volterra integral equations of the second kind and how we can approximate it. For this, we analyse the role played by the Banach Contraction Principle to locate a solution and its approximation by the method of successive approximations. We improve the previous analysis by giving a location of the solution and then approximate it by a collocation method that uses Lagrange polynomials. To avoid the Runge phenomenon that may appear when the number of nodes increases, we choose the Chebyshev zeros as the collocation points. But, when increasing the number of nodes to improve the precision, the problem of possible ill-conditioning of the linear system involved in the collocation method may arise. This last problem is solved by applying an inverse-free iterative method that uses only matrix products.

Suggested Citation

  • Ezquerro, J.A. & Hernández-Verón, M.A. & Magreñán, Á.A. & Moysi, A., 2024. "On the existence and the approximation of solutions of Volterra integral equations of the second kind," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    • Handle: RePEc:eee:apmaco:v:478:y:2024:i:c:s009630032400290x
    DOI: 10.1016/j.amc.2024.128829
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