We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent...

We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence relevant finite-element provide theoretical estimate error. conclude with some numerical experiments further support results.

Abstract This paper describes an experiment that attempts to compare a range of existing collocation extraction techniques as well as the implementation of a new technique based on tests for lexical substitutability. After a description of the experiment details, the techniques are discussed with particular emphasis on any adaptations that are required in order to evaluate it in the way propose...

Abstract: Multivariate polynomial metamodels are widely used for uncertainty quantification due to the development of polynomial chaos methods and stochastic collocation. However, these metamodels only provide point predictions. There is no known method that can quantify interpolation error probabilistically and design interpolation points using available data to reduce the error. We shall intr...

We studied the source localization accuracy in MEG with single-surface brain-shaped conductor models. The Galerkin method with linear basis functions was used as a discretization method. To Þnd a dipolar source, a variant of the Newton method was used for solving nonlinear least-squares problems. Reference magnetic Þelds were computed using a very large number of unknowns to obtain accurate sol...

In this work, we describe a numerical method which enables an efficient computation of membrane gas permeation processes that involve multiple membrane stages and multiple gas components. The utilized numerical approach is a collocation method equipped with a grid adaptation strategy based on a dependable error estimate of the numerical approximation. The comparison of the results provided by t...

The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of along illustrated. numerical algorithm provided based collocation method and Tikhonov regularization. estimates parabolic hyperbolic are demonstrated by examples respectively.

Abstract: In this paper, a new operational matrix method based on the Taylor polynomials is presented to solve generalized pantograph type delay differential equations. The method is based on operational matrices of integration and product for Taylor polynomials. These matrices are obtained by using the best approximation of function by the Taylor polynomials. The advantage of the method is tha...

In this paper, the system of Fredholm integral equations of the second kind is investigated by using a modified degenerate kernel  method (MDKM). To construct a MDKM the source function is approximated by the same way of producing degenerate kernel. The interpolation is used to make the needed approximations. Lagrange polynomials are adopted for the interpolation. The equivalency of  proposed m...

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...