BACKGROUND Infectious disease outbreaks in communities can be controlled by early detection and effective prevention measures. Assessing the relative importance of each individual community member with respect to these two processes requires detailed knowledge about the underlying social contact network on which the disease can spread. However, mapping social contact networks is typically too r...

This work proposes and analyzes an anisotropic sparse grid stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms (input data of the model). The method consists of a Galerkin approximation in the space variables and a collocation, in probability space, on sparse tensor product grids utilizing either Clenshaw-Curtis or Gaussia...

This paper describes a system of terminological extraction capable of handling multi-word expressions, using a powerful syntactic parser. The system includes a concordancing tool enabling the user to display the context of the collocation, i.e. the sentence or the whole document where the collocation occurs. Since the corpora are multilingual, the system also offers an alignment mechanism for t...

We introduce isogeometric collocation methods based on generalized B-splines and we analyze their performance through numerical examples for univariate and multivariate scalarand vector-valued problems. In particular, advection–diffusion and linear elasticity model problems are addressed. The resultingmethod combines the favorable properties of isogeometric collocation and the geometrical and a...

The computation schemes of spline-collocation methods for solving singular integral equations. A theoretical foundation of these two methods is obtained in space L2. In the present paper we give theoreticaly justification of the numerical schemes of spline-collocation method for solving the singular integral equations (SIE) of the following form

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena. AMS subject cla...

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium in non-periodic space. The concentration is treated by a characteristics collocation method, while the pressure is treated by a finite element collocation method. Optimal order estimates in L2 is derived.

We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3spheres. Besides the main ideas, we discuss issues related to our implementation and analyze numerical test applications. Our main interest lies in cosmological solutions of Einstein’s field equations. Motivated by this, we also elab...

In this paper, we improve b-spline collocation method for Benjamin-Bona-Mahony-Burgers (BBMB) by using defect correction principle. The exact finite difference scheme is used to find defect and the defect correction principle is used to improve collocation method. The method is tested on somemodel problems and the numerical results have been obtained and compared.