Algorithm 876
Algorithm 876: Solving Fredholm integral equations of the second kind in Matlab. We present here the algorithms and user interface of a Matlab program, Fie, that numerically solves Fredholm integral equations of the second kind on an interval [a,b] to a specified, modest accuracy. The kernel function K(s,t) is to be moderately smooth on [a;b]×[a;b] except possibly across the diagonal s=t. If the interval is finite, Fie provides for kernel functions that behave in a variety of ways across the diagonal, viz. K(s,t) may be smooth, have a discontinuity in a low-order derivative, have a logarithmic singularity, or have an algebraic singularity. Fie also solves a large class of integral equations with moderately smooth kernel function on [0,1).
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 13 articles , 1 standard article )
Showing results 1 to 13 of 13.
Sorted by year (- Rahmoune, Azedine: On the numerical solution of integral equations of the second kind over infinite intervals (2021)
- Rakshit, Gobinda; Rane, Akshay S.: Asymptotic expansion of iterated Galerkin solution of Fredholm integral equations of the second kind with Green’s kernel (2020)
- Zhang, Yang-Hong; Chen, Jiao-Kai: Error estimates for the nearly singular momentum-space bound-state equations (2020)
- Brezinski, Claude; Redivo-Zaglia, Michela: Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations (2019)
- Dimov, I. T.; Maire, S.: A new unbiased stochastic algorithm for solving linear Fredholm equations of the second kind (2019)
- Betz, Wolfgang; Papaioannou, Iason; Straub, Daniel: Numerical methods for the discretization of random fields by means of the Karhunen-Loève expansion (2014)
- Korkmaz, Nebiye; Güney, Zekeriya: An adaptive approach to solutions of Fredholm integral equations of the second kind (2014)
- Li, Shengguo; Gu, Ming; Cheng, Lizhi: Fast structured LU factorization for nonsymmetric matrices (2014)
- Krämer, Walter: High performance verified computing using C-XSC (2013)
- Kulkarni, Rekha P.; Rane, Akshay S.: Asymptotic expansions for approximate eigenvalues of integral operators with nonsmooth kernels (2012)
- Atkinson, Kendall: A personal perspective on the history of the numerical analysis of Fredholm integral equations of the second kind (2010)
- Peng, Xu-long; Li, Xian-fang: Thermoelastic analysis of functionally graded annulus with arbitrary gradient (2009)
- Atkinson, Kendall E.; Shampine, Lawrence F.: Algorithm 876: Solving Fredholm integral equations of the second kind in Matlab. (2008)