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Open AccessArticle

On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations

Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Symmetry 2019, 11(10), 1200; https://doi.org/10.3390/sym11101200
Received: 6 September 2019 / Revised: 21 September 2019 / Accepted: 23 September 2019 / Published: 24 September 2019
(This article belongs to the Special Issue Fixed Point Theory and Computational Analysis with Applications)
In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra–Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence and uniqueness of the solution (results which also provide successive iterations of the solution) and suitable cubature formulas for the numerical approximations. We discuss in detail a method using Picard iteration and the two-dimensional composite trapezoidal rule, giving convergence conditions and error estimates. The paper concludes with numerical experiments and a discussion of the methods proposed. View Full-Text
Keywords: mixed Volterra–Fredholm integral equations; fixed-point theory; Picard iteration; numerical approximation; cubature formulas mixed Volterra–Fredholm integral equations; fixed-point theory; Picard iteration; numerical approximation; cubature formulas
MDPI and ACS Style

Micula, S. On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations. Symmetry 2019, 11, 1200.

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