Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries

Numerical methods for Fredholm integral equations with singular right-hand sides

Fredholm integral equations with the right-hand side having singularities at the endpoints are considered. The singularities are moved into the kernel that is subsequently regularized by a suitable one-to-one map. The Nyström method is applied to the regularized equation. The convergence, stability and well conditioning of the method is proved in spaces of weighted continuous functions. The spe...

Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

New iterative method for solving linear Fredholm fuzzy integral equations of the second kind

A new method for solving two-dimensional fuzzy Fredholm integral equations of the second kind

In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equations of the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and convert a two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equations of the second kind in crisp case. We can use Adomian decomposition method for n...

Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems

The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp)‎. ‎The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system‎. ‎In this article‎, ‎the obtained nonlinear system has been solved as a dynamical system‎. ‎The solution of the obtained nonlinear system by the dynamical system throug...