The discrete Galerkin method for 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...

The Discrete Galerkin Method for Nonlinear Integral Equations

Let K be a completely continuous nonlinear integral operator, and consider solving x = K(x) by Galerkin's method. This can be written as xn = PnK(xn),Pn an orthogonal projection; the iterated Galerkin solution is defined by xn = K(xn). We give a general framework and error analysis for the numerical method that results from replacing all integrals in Galerkin's method with numerical integrals. ...

Superconvergence Results for the Iterated Discrete Legendre Galerkin Method for Hammerstein Integral Equations

In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equation with a smooth kernel. Using a sufficiently accurate numerical quadrature rule, we obtain super-convergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and L-norm. Numerical examples are given to illustrate the theoretical results.

Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

Fuzzy Galerkin method for solving Fredholm integral equations with error analysis