Discrete Polynomial-Based Galerkin Methods for Fredholm Integral Equations

The Discrete Galerkin Method for Integral Equations

A general theory is given for discretized versions of the Galerkin method for solving Fredholm integral equations of the second kind. The discretized Galerkin method is obtained from using numerical integration to evaluate the integrals occurring in the Galerkin method. The theoretical framework that is given parallels that of the regular Galerkin method, including the error analysis of the sup...

Fuzzy Galerkin method for solving Fredholm integral equations with error analysis

A New Polynomial Method for Solving Fredholm –Volterra Integral Equations

Abstract— A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some num...

Galerkin Methods for Singular Integral Equations

The approximate solution of a singular integral equation by Galerkin's method is studied. We discuss the theoretical aspects of such problems and give error bounds for the approximate solution.

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...