Numerical simulations of extereme mass ratio inspirals, the mostimportant sources for LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation theory and calculations self-force acting on point particles orbiting supermassive holes. Such are distributionally sourced, standard numerical methods...

Collocation translation is important for machine translation and many other NLP tasks. Unlike previous methods using bilingual parallel corpora, this paper presents a new method for acquiring collocation translations by making use of monolingual corpora and linguistic knowledge. First, dependency triples are extracted from Chinese and English corpora with dependency parsers. Then, a dependency ...

Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided design and engineering, which has been widely applied in various aspects of computational mechanics. IGA involves Galerkin collocation formulations. Exploiting the same high-order non-uniform rational B-spline (NURBS) bases that span physical domain solution space leads to increased accuracy fast computat...

will be employed in the analysis of the principle properties of the collocation approximations; the extension to nonlinear equations is straightforward (cf. [1, p. 225]). High-order numerical methods for VIDEs with weakly singular kernels may be found in [1,2,6,7,8]. In this note we shall consider collocation methods for VIDE (1.1), based on Brunner's approach [1]. The following method and nota...

In this paper we present a new method of automatic collocation identification. Collocation is an important relation between words, which is widely used, among others, in information retrieval tasks. Over the last years, many methods of automatic collocation acquisition from text corpora have been proposed. The approach described in this paper differs from the others by focusing on domain colloc...

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...