Collocation methods are popular in providing numerical approximations to complicated governing equations owing to their simplicity in implementation. However, point collocation methods have limitations regarding accuracy and have been modified upon with the application of B-spline approximations. The present study reports the stress and deformation behavior of shear deformable functionally grad...

In this paper we introduce a measure for calculating statistically significant collocation sets that is related to the Poisson distribution. We show that results calculated using this measure are comparable to well-known measures like the log-likelihood measure. Additionally, we discuss asymptotic behaviour and additivity as general properties of the measure which may be applied to the analysis...

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...

The Meshless Local Petrov-Galerkin (MLPG) “mixed collocation” method is applied to the problem of topology-optimization of elastic structures. In this paper, the topic of compliance minimization of elastic structures is pursued, and nodal design variables which represent nodal volume fractions at discretized nodes are adopted. A so-called nodal sensitivity filter is employed, to prevent the phe...

We show that various (discrete) methods for the approximate solution of Volterra (and Abel) integral equations of the first kind correspond to some discrete version of the method of (recursive) collocation in the space of (continuous) piecewise polynomials. In a collocation method no distinction has to be made between equations with regular or weakly singular kernels; the regularity or nonregul...

Although multiword expressions (MWEs) have received an increasing amount of attention in the NLP community over the last two decades, few papers have been dedicated to the specific problem of the interaction between MWEs and parsing. In this paper, we will discuss how the collocation identification task has been integrated in our rulebased parser and show how collocation knowledge has a positiv...

Our main objective in participating MUC-7 is to investigate and experiment with the use of collocation statistics in information extraction. A collocation is a habitual word combination, such as \weather a storm", \ le a lawsuit", and \the falling yen". Collocation statistics refers to the frequency counts of the collocational relations extracted from a parsed corpus. For example, out of 6577 i...

In this article, we have investigate a Taylor collocation method, which is based on collocation method for solving fractional pantograph equation. This method is based on first taking the truncated fractional Taylor expansions of the solution function in the mathematical model and then substituting their matrix forms into the equation. Using the collocation points, we have the system of nonline...