Journal ArticleDOI
The Numerical Evaluation of Fixed Points for Completely Continuous Operators
TLDR
In this paper, a completely continuous nonlinear operator on a domain D contained in a Banach space is given, and a common way of approximating this operator leads to a sequence of nonlinear operators.Abstract:
Given a completely continuous nonlinear operator $\mathcal{K}$ on a domain D contained in a Banach space $\mathcal{X}$, one common way of approximating $\mathcal{K}$ leads to a sequence $\{ \mathca...read more
Citations
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Journal ArticleDOI
A Survey of Numerical Methods for Solving Nonlinear Integral Equations
TL;DR: A survey of numerical methods for calculating fixed points of nonlinear integral operators is given in this article, where the emphasis is on general methods, ones that are applicable to a wide variety of non-linear integral equations.
Journal ArticleDOI
Projection and iterated projection methods for nonliear integral equations
TL;DR: In this article, the convergence of the Urysohn integral operators to the Galerkin and collocation methods was analyzed for a large class of integral operators in one variable.
Journal ArticleDOI
A meshless method for solving nonlinear two-dimensional integral equations of the second kind on non-rectangular domains using radial basis functions with error analysis
TL;DR: A numerical method for solving two-dimensional nonlinear Fredholm integral equations of the second kind on a non-rectangular domain using radial basis functions constructed on scattered points as a basis in the discrete collocation method.
Journal ArticleDOI
Iterative variants of the Nyström method for the numerical solution of integral equations
TL;DR: Some iterative variants of the Nystrom method for numerical solution of linear and nonlinear integral equations are introduced and discussed in this article, where numerical examples are given; some are for integral equations with singular kernel functions.
Journal ArticleDOI
Application of Sinc-collocation method for solving a class of nonlinear Fredholm integral equations
TL;DR: These numerical methods combine a Sinc collocation method with the Newton iterative process that involves solving a nonlinear system of equations to improve conventional results and achieve exponential convergence of the nonlinear Fredholm integral equations.
References
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Journal ArticleDOI
Über Die Praktische Auflösung von Integralgleichungen mit Anwendungen auf Randwertaufgaben
Journal ArticleDOI
The Numerical Solution of Fredholm integral Equations of the Second Kind
TL;DR: When the kernel has several continuous derivatives, the method reduces to replacing the integral with a numerical integral and then to solving a finite linear system; see as discussed by the authors for a generalized form of numerical inltegration for functioins of oine variable.