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...

We discuss an a-posteriori error estimate for the numerical solution of boundary value problems for nonlinear systems of ordinary differential equations with a singularity of the first kind. The estimate for the global error of an approximation obtained by collocation with piecewise polynomial functions is based on the defect correction principle. We prove that for collocation methods which are...

In this paper, we develop a Jacobi-Gauss-Lobatto collocation method for solving the nonlinear fractional Langevin equation with three-point boundary conditions. The fractional derivative is described in the Caputo sense. The shifted Jacobi-Gauss-Lobatto points are used as collocation nodes. The main characteristic behind the Jacobi-Gauss-Lobatto collocation approach is that it reduces such a pr...

Introduction Importance of collocation in efficient language learning is well recognized in the domain of second language education. In recent years investigations in brain science shows that retrieving from mental lexicon words acquired in conventional text-based learning is significantly slower on the scene of actual setting than those obtained in situationbased learning[1]. This paper adopts...

The paper describes ongoing work on the evaluation of methods for extracting collocation candidates from large text corpora. Our research is based on a German treebank corpus used as gold standard. Results are available for adjective+noun pairs, which proved to be a comparatively easy extraction task. We plan to extend the evaluation to other types of collocations (e.g., PP+verb pairs).

Fast direct methods are presented for the solution of linear systems arising in highorder, tensor-product orthogonal spline collocation applied to separable, second order, linear, elliptic partial di erential equations on rectangles. The methods, which are based on a matrix decomposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline co...

Arbitrary recurrent word combinations (collocations) are a key in language learning. However, even advanced students have difficulties when using them. Efficient collocation aiding tools would be of great help. Still, existing “collocation checkers” still struggle to offer corrections to miscollocations. They attempt to correct without making any distinction between the different types of error...

A Multistep collocation techniques is used in this paper to develop a 3-point explicit and implicit block methods, which are suitable for generating solutions of the general second-order ordinary differential equations of the form y′′ f x, y, y′ , y x0 a, y′ x0 b. The derivation of both explicit and implicit block schemes is given for the purpose of comparison of results. The Stability and Conv...