A numerical method for solving second order, transient, parabolic partial differential equation is presented. The spatial discretization is based on Hermite collocation method (HCM). It is a combination of orthogonal collocation method and piecewise cubic Hermite interpolating polynomials. The solution is obtained in terms of cubic Hermite interpolating basis. Numerical results have been plotte...

We investigate the stochastic collocation method for parametric, elliptic partial differential equations (PDEs) with lognormally distributed random parameters in mixed formulation. Such problems arise, e.g., in uncertainty quantification studies for flow in porous media with random conductivity. We show the analytic dependence of the solution of the PDE w.r.t. the parameters and use this to sho...

We describe a mesh selection strategy for the numerical solution of boundary value problems for singular ordinary differential equations. This mesh adaptation procedure is implemented in our MATLAB code sbvp which is based on polynomial collocation. We prove that under realistic assumptions our mesh selection strategy serves to approximately equidistribute the global error of the collocation so...

A description of a system for measuring the compositionality of collocations within the framework of the shared task of the Distributional Semantics and Compositionality workshop (DISCo 2011) is presented. The system exploits the intuition that a highly compositional collocation would tend to have a considerable semantic overlap with its constituents (headword and modifier) whereas a collocatio...

This paper reports a new spectral collocation algorithm for solving time-space fractional partial differential equations with subdiffusion and superdiffusion. In this scheme we employ the shifted Legendre Gauss-Lobatto collocation scheme and the shifted Chebyshev Gauss-Radau collocation approximations for spatial and temporal discretizations, respectively. We focus on implementing the new algor...

The change in orbit evolution between collocated satellites (X, Y) inside +/-0.09° E/W and +/0.07° N/S cluster, after one of these satellites is placed in an inclined orbit (satellite X) and the effect of this change in the collocation safety inside the cluster window has been studied and evaluated. Several collocation scenarios had been studied in order to adjust the location of both satellite...

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the e...

In this paper, an approach based on statistical spline model (SSM) and collocation method is proposed to solve Volterra-Fredholm integral equations. The set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials. Under some standard assumptions, we establish the convergence property of this approach. Numerical results on some problems are given to describ...

The work presented provides computational linguistics methods and tools for collocation identiication from arbitrary text, and methods and tools for representing collocations in a relational database integrating competence (collocation-type-speciic linguistic analysis) and performance information (corpus sentences). The work diiers from existing approaches to collo-cation identiication in syste...

Techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau, and least-squares methods, are adopted to solve a non-linear and highly coupled pellet problem. Based on a residual measure and problem matrix condition numbers, the Galerkin and tau methods are favorable solution techniques for the pellet equations. On the other hand, the orthogonal collocation is...