Solving second kind integral equations by Galerkin methods with continuous orthogonal wavelets

Galerkin Methods for Second Kind Integral Equations

This paper discusses the numerical solution of Fredholm integral equations of the second kind which have weakly singular kernels and inhomogeneous terms. Global convergence estimates are derived for the Galerkin and iterated Galerkin methods using splines on arbitrary quasiuniform meshes as approximating subspaces. It is observed that, due to the singularities present in the solution being appr...

Wavelet Galerkin methods for second-kind integral equations

We use vector-valued multiwavelets on compact sets to develop a Galerkin method for systems of integral equations of the second kind. We propose a compression strategy for the coeflieient matrix of the linear system obtained from this method and show that the compressed scheme preserves almost optimal convergence rate of the original scheme and yields a sparse matrix with a bounded condition nu...

Solving Fuzzy Integral Equations of the Second Kind by Fuzzy Laplace Transform Method

Solving Linear Fred Holm Fuzzy Integral Equations of the Second Kind by Modified Trapezoidal Method

One of the methods for solving definite integrals is modified trapezoid method, which is obtained by using Hermitian interpolation (see e.g. [12]). In this article, we have used modified trapezoid quadrature method and Generalized differential to solve the Fredholm fuzzy integral equations of the second kind. This method leads to solve fuzzy linear system. Finally the proposed method is illustr...

Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind

In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is car...