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On some iterative numerical methods for a Volterra functional integral equation of the second kind

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Abstract

In this paper, we study an iterative numerical method for approximating solutions of a certain type of Volterra functional integral equations of the second kind (Volterra integral equations where both limits of integration are variables). The method uses the contraction principle and a suitable quadrature formula. Under certain conditions, we prove the existence and uniqueness of the solution and give error estimates for our approximations. We also included a numerical example which illustrates the fast approximations.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

    Sanda Micula

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  1. Sanda Micula
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Correspondence to Sanda Micula.

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Micula, S. On some iterative numerical methods for a Volterra functional integral equation of the second kind. J. Fixed Point Theory Appl. 19, 1815–1824 (2017). https://doi.org/10.1007/s11784-016-0336-6

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  • DOI: https://doi.org/10.1007/s11784-016-0336-6

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