This report is devoted to the study and to the comparison of methods for estimation of the local error and for adaptive step-size control when solving the generalised nonlinear Schrodinger equation (GNLSE) in optics by the Interaction Picture (IP) method or by the Symmetric Split-Step (S3F) method. Namely, we propose and study the use of an embedded Runge-Kutta method to solve the nonlinear pro...

In this paper, we develop the a posteriori error estimation of hp-version interior penalty discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders. A series of numerical experiments il...

We present techniques of a posteriori error estimation for Q1 finite element discretizations based on residual evaluations with respect to test functions of higher-order. This technique is designed for quadrilateral (or hexahedral) triangulations and gives local error indicators in terms of nodal contributions. We show reliability and efficiency of the estimator. Moreover, we present a simplifi...

This paper discusses the development of a particle filter for attitude and angular rate estimation of a space object using light curve observations. The particle filter approach used is based on the generalized Rodrigues parameters (GRPs) local error representation. The global state used is the quaternion to avoid singularity in the attitude states. Uniform quaternions are generated to approxim...

We present an algorithm for parameter identification in combustion problems modelled by partial differential equations. The method includes local mesh refinement controlled by a posteriori error estimation with respect to the error in the parameters. The algorithm is applied to two types of combustion problems. The first one deals with the identification of Arrhenius parameters, while in the se...

When preparing a design model for engineering analysis, model idealization is often used, where defeaturing, and/or local dimension reduction of thin regions, are carried out. This simplifies the analysis, but quantitative estimates of the idealization error, the analysis error caused by this idealization, are necessary if the results are to be of practical use. The paper focuses on a posterior...

this paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. finally an example is given to illustrate the performance of the methods.

Nonparametric methods play a central role in modern empirical work. While they provide inference procedures that are more robust to parametric misspecification bias, they may be quite sensitive to tuning parameter choices. We study the effects of bias correction on confidence interval coverage in the context of kernel density and local polynomial regression estimation, and prove that bias corre...

Because of the limited approximation capability of using fixed basis functions, the performance of reflectance estimation obtained by traditional linear models will not be optimal. We propose an approach based on the regularized local linear model. Our approach performs efficiently and knowledge of the spectral power distribution of the illuminant and the spectral sensitivities of the camera is...

We present a weighted residual scheme for estimation of pointwise gradient errors in finite element methods for quasilinear elliptic problems. First we define computable residual weights which may be conveniently determined using local ellipticity properties of the underlying differential operator. Using a combination of theoretical and computational results, the resulting a posteriori error es...