This article investigates the stability of the collocation method for the Radiosity equation. We introduce graded meshes and trial spaces of piecewise poynomials and prove stability for some modified collocation method. Next we show that graded meshes are necessary, even for linear convergence. The generation of triangulations which allow higher order approximations leads to geometrical problem...

This study evaluates the impact of integrating two different collocation segmentations methods in a standard phrase-based statistical machine translation approach. The collocation segmentation techniques are implemented simultaneously in the source and target side. Each resulting collocation segmentation is used to extract translation units. Experiments are reported in the English-to-Spanish Bi...

‎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...

: This study investigated the impact of audio-visual input enhancement teaching techniques on improving English as Foreign Language (EFL) learnersˈ collocation learning as well as their accuracy concerning collocation use in narrative writing. In addition, it compared the impact and efficiency of audio-visual input enhancement in two learning contexts, namely traditional and mo...

the most important and practical phase of analyzing the linguistic errors of second language learners is to find the solutions to decrease these errors. to that end, the present study examined translation strategy to decrease the number of grammatical and lexical errors of chinese language learners learning persian. twelve chinese language learners were asked to write a text in two stages. firs...

The von-K arm an nonlinear, dynamic, partial differential system over rectangular domains is considered, and numerically solved using both the Chebyshev-collocation and Legendre-collocation methods for the spatial discretization and the implicit Newmark-b scheme combined with a non-linear fixed point algorithm for the temporal discretization. As the system is non-linear, involving operators of ...

Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic ...

The commonly used graded piecewise polynomial collocation method for weakly singular Volterra integral equations may cause serious round-off error problems due to its use of extremely nonuniform partitions and the sensitivity of such time-dependent equations to round-off errors. The singularity preserving (nonpolynomial) collocation method is known to have only local convergence. To overcome th...