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

Symmetry

Sanda Micula¹ 

[1] Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania;

关键词: mixed Volterra–Fredholm integral equations;    fixed-point theory;    Picard iteration;    numerical approximation;    cubature formulas;   

DOI  :  10.3390/sym11101200

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown