Extrapolation of the Iterated–Collocation Method for Integral Equations of the Second Kind

Asymptotic error expansion for the Nyström method for nonlinear Fredholm integral equations of the second kind

“…example [1]- [3] [6] give a one-term asymptotic error expansion for the iterated collocation method of a Fredholm integral equation on an arbitrary mesh. In this paper, we consider the nonlinear Fredholm integral equation of the second kind, and we obtain an asymptotic error expansion for the NystrSm solution of (1.1).…”

Richardson Extrapolation and Defect Correction of Mixed Finite Element Methods for Elliptic Optimal Control Problems

“…The effectiveness of this technique relies heavily on the existence of an asymptotic expansion for the error. This technique has been well demonstrated in its applications to the finite element and the mixed finite element methods for elliptic partial differential equations [4,6,22,34,35], parabolic partial differential equations [18], integral and integro-differential equations [22,24,25,26,38], and to the boundary element methods and collocation methods in [37] and [21], respectively. The defect correction (Galerkin and Petrov-Galerkin) finite element by means of an interpolation postprocessing technique is another numerical method to obtain approximations of higher accuracy, which has been proved for a wide variety of models, see, for example, [22,23,5], and the references cited therein.…”

Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media

“…As an efficient numerical method to increase the accuracy of approximations, Richardson extrapolation has been demonstrated in [29] for the difference method, in [3], [5], [8], [15], [19], [21]- [25], [26], [34], [35], [37], [38] for the (Galerkin and Petrov-Galerkin) finite element method and the mixed finite element method, in [18] and [36] for the collocation method and the boundary element method, respectively.…”