In this paper a new method for solving (non-linear) ordinary differential equations is proposed. The method is based on finite elements (collocation method) as well as on genetic algorithms. The method seems to have some advantages in comparison with the typical sequential (one – step and multi – step) methods. Key-Words: Ordinary Differential Equations, Finite Elements, Genetic Algorithms, Evo...

The aim of this paper is to carry out a rigorous error analysis for the Strang splitting Laguerre–Hermite/Hermite collocation methods for the time-dependent Gross–Pitaevskii equation (GPE). We derive error estimates for full discretizations of the three-dimensional GPE with cylindrical symmetry by the Strang splitting Laguerre–Hermite collocation method, and for the d-dimensional GPE by the Str...

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

This report evaluates the impact of using a novel collocation segmentation method for phrase extraction in the standard phrase-based statistical machine translation approach. The collocation segmentation technique is implemented simultaneously in the source and target side. The resulting collocation segmentation is used to extract translation units. Experiments are reported in the Spanish-toEng...

In this work we present numerical methods for the solution of Fredholm integral equations of the second type for smooth and piecewise smooth surfaces We use a collocation method based on piecewise polynomial interpolation of the solution We consider only collocation methods for which the collocation nodes are interior to each triangular face In Chapter II we give the general framework for collo...