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...

Nowadays, spaceborne Synthetic Aperture Radar (SAR) has become a powerful tool for providing significant wave height. Traditionally, validation of SAR derived ocean wave height has been carried out against buoy measurements or model outputs, which only yield a inter-comparison, but not an ‘absolute’ validation. In this study, the triple collocation error model has been introduced in the validat...

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least-squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least-squares functional associated...

Multiword terms (MWTs) are relevant strings of words in text collections. Once they are automatically extracted, they may be used by an Information Retrieval system, suggesting its users possible conceptual interesting refinements of their information needs. As a matter of fact, these multiword terms point to relevant information, often corresponding to topics and subtopics in the text collecti...

Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial ...

Abstract: Multivariate polynomial metamodels are widely used for uncertainty quantification due to the development of polynomial chaos methods and stochastic collocation. However, these metamodels only provide point predictions. There is no known method that can quantify interpolation error probabilistically and design interpolation points using available data to reduce the error. We shall intr...

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary differential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate. Received: 2 February 2014, Revised: 4 May 201...

Some of the most widely used algorithms for two-point boundary value ODEs, namely nite diierence and collocation methods and standard multiple shooting, proceed by setting up and solving a structured system of linear equations. It is well known that the linear system can be set up eeciently in parallel; we show here that a structured orthogonal factorization technique can be used to solve this ...

Collocations in the sense of idiosyncratic binary lexical co-occurrences are one of the biggest challenges for any language learner. Even advanced learners make collocation mistakes in that they literally translate collocation elements from their native tongue, create new words as collocation elements, choose a wrong subcategorization for one of the elements, etc. Therefore, automatic collocati...