Article history: Received 10 March 2014 Received in revised form 12 November 2014 Accepted 1 December 2014 Available online 9 December 2014

The problem of the boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is considered. A spectral collocation method is performed in order to find an analytical solution of the governing nonlinear differential equations. The obtained results are finally compared through the illustrative graphs and tables with the exact solution and some well-known results ob...

The numerical solution of boundary value problems for ordinary differential equations on infinite intervals is considered. The infinite interval is cut at a finite, large enough point and additional boundary conditions are posed there. For the solution of the resulting problem, /(-stable symmetric collocation methods are employed. Using the behavior of the solution of the "infinite" problem, me...

This paper focuses on the use of advanced techniques of text analysis as support for collocation extraction. A hybrid system is presented that combines statistical methods and multilingual parsing for detecting accurate collocational information from English, French, Spanish and Italian corpora. The advantage of relying on full parsing over using a traditional window method (which ignores the s...

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...