Search results for "collocation"

A Spline Collocation Scheme for the Spherical Shallow Water Equations

1999

A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations

2021

Abstract In this work, a matrix method based on Laguerre series to solve singularly perturbed second order delay parabolic convection-diffusion and reaction-diffusion type problems involving boundary and initial conditions is introduced. The approximate solution of the problem is obtained by truncated Laguerre series. Moreover convergence analysis is introduced and stability is explained. Besides, a test case is given and the error analysis is considered by the different norms in order to show the applicability of the method.

On the stability of spline-collocation methods of multivalue type

1987

In this paper the general classV of spline-collocation methods for first order systems of ordinary differential equations is investigated. The methods can in part be regarded as so-called multivalue methods. This type contains the generalized singly-implicit methods treated by Butcher.

A-stable spline-collocation methods of multivalue type

1989

In this paper the general classV of spline-collocation methods presented by Multhei is investigated. The methods ofV approximate solutions of first order initial value problems. ClassV contains as subclass the methods of so-called multivalue type, and in particular contains the generalized singly-implicit methods treated by Butcher.

On the stability of the collocation method for the double layer operator on polyhedral domains in R3

2002

Towards a novel approach for Sentinel-3 synergistic OLCI/SLSTR cloud and cloud shadow detection based on stereo cloud-top height estimation

2021

Abstract Sentinel-3 is an Earth observation satellite constellation launched by the European Space Agency. Each satellite carries two optical multispectral instruments: the Ocean and Land Colour Instrument (OLCI) and the Sea and Land Surface Temperature Radiometer (SLSTR). OLCI and SLSTR sensors produce images covering the visible and infrared spectrum that can be collocated in order to generate synergistic products. In Earth observation, a particular weakness of optical sensors is their high sensitivity to clouds and their shadows. An incorrect cloud and cloud shadow detection leads to mistakes in both land and ocean retrievals of biophysical parameters. In order to exploit both OLCI and S…

Hierarchical fast BEM for anisotropic time-harmonic 3-D elastodynamics

2012

The paper presents a fast boundary element method for anisotropic time-harmonic 3-D elastodynamic problems. The approach uses the hierarchical matrices format and the ACA algorithm for the collocation matrix setup and a preconditioned GMRES solver for the solution. The development of this approach for the anisotropic case presents peculiar aspects which deserve investigation and are studied in the paper leading to the employed computational strategy and its effective tuning. Numerical experiments are presented to assess the method accuracy, performances and numerical complexity. The method ensures adequate accuracy allowing remarkable reductions in computation time and memory storage.

Korpusavusteinen diskurssintutkimus (CADS): analyysiesimerkki homouden ja heterouden digitaalisista diskursseista

2018

The article aims at combining two methodological approaches, namely corpus linguistics and discourse studies. Both of these approaches are present in corpus-assisted discourse studies (CADS) which makes use of both quantitative and qualitative methodologies. First, an attempt is made to discuss the differences and similarities of these two traditions based on Leech’s (2000) listing. However, it turns out that this listing does not include all necessary viewpoints, and those are further discussed. In the empirical section of the paper, the Suomi24 corpus is analysed in order to provide an example of CADS. The analysis was carried out through collocation and discourse prosody analyses. The re…

A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

2014

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains (Ciraolo et al. in J Comput Phys 246:78–95, 2013) where the index of refraction is not required to be constant at infinity. The approach is based on the minimization of an integral functional, which arises from an integral formulation of the radiation condition at infinity. In this paper, we implement a Fourier–Chebyshev collocation method to study some convergence properties of the numerical algorithm; in particular, we give numerical evidence of some convergence estimates available in the literature (Ciraolo in Helmholtz equation in unbou…

Hybrid approximation for solutions of high-order integro-differential equations including variable delay

2020

Abstract In this study, a numerical technique with hybrid approximation is developed for solving high-order linear integro-differential equations including variable delay under the initial conditions. These type of problems are of applications in mathematical physics, mechanics, natural sciences, electronics and computer science. The aim of this work is to investigate an approximation with the matrix forms of Taylor and Laguerre polynomials along with standard collocation points. By the reduction of the solution of this problem with regard to the matrix relations, the solution of a system of algebraic equations has been obtained. The usefulness of this algorithm has been demonstrated by num…