Numerical Solutions for second-kind Volterra integral equations by Galerkin methods

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...

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

Numerical method for non-linear fuzzy Volterra integral equations of the second kind

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...

Numerical solution for Fredholm–Volterra integral equation of the second kind by using collocation and Galerkin methods

The Fredholm–Volterra integral equation of the second kind with continuous kernels with respect to position and time, is solved numerically, using the Collocation and Galerkin methods. Also the error, in each case, is estimated.