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.


References in zbMATH (referenced in 11 articles , 1 standard article )

Showing results 1 to 11 of 11.
Sorted by year (citations)

  1. Zhang, Yang-Hong; Chen, Jiao-Kai: Error estimates for the nearly singular momentum-space bound-state equations (2020)
  2. Brezinski, Claude; Redivo-Zaglia, Michela: Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations (2019)
  3. Dimov, I. T.; Maire, S.: A new unbiased stochastic algorithm for solving linear Fredholm equations of the second kind (2019)
  4. Betz, Wolfgang; Papaioannou, Iason; Straub, Daniel: Numerical methods for the discretization of random fields by means of the Karhunen-Loève expansion (2014)
  5. Korkmaz, Nebiye; Güney, Zekeriya: An adaptive approach to solutions of Fredholm integral equations of the second kind (2014)
  6. Li, Shengguo; Gu, Ming; Cheng, Lizhi: Fast structured LU factorization for nonsymmetric matrices (2014)
  7. Krämer, Walter: High performance verified computing using C-XSC (2013)
  8. Kulkarni, Rekha P.; Rane, Akshay S.: Asymptotic expansions for approximate eigenvalues of integral operators with nonsmooth kernels (2012)
  9. Atkinson, Kendall: A personal perspective on the history of the numerical analysis of Fredholm integral equations of the second kind (2010)
  10. Peng, Xu-long; Li, Xian-fang: Thermoelastic analysis of functionally graded annulus with arbitrary gradient (2009)
  11. Atkinson, Kendall E.; Shampine, Lawrence F.: Algorithm 876: Solving Fredholm integral equations of the second kind in Matlab. (2008)