Search results for "Collocation"

Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

2011

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.

Non-Lipschitz Homogeneous Volterra Integral Equations

2018

In this chapter we introduce a class of nonlinear Volterra integral equations (VIEs) which have certain properties that deviate from the standard results in the field of integral equations. Such equations arise from various problems in shock wave propagation with nonlinear flux conditions. The basic equation we will consider is the nonlinear homogeneous Hammerstein–Volterra integral equation of convolution type $$\displaystyle u(t) = \int _0^t k(t-s) g(u(s))\,\mathrm {d}s. $$ When g(0) = 0, this equation has function u ≡ 0 as a solution (trivial solution). It is interesting to determine whether there exists a nontrivial solution or not. Classical results on integral equations are not to be …

A fast dual boundary element method for 3D anisotropic crack problems

2009

In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical …

Exponential convergence andH-c multiquadric collocation method for partial differential equations

2003

The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocatethe approximate solution of PDEs. It is a truly meshless method as compared to some of the so-calledmeshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are twoways to make the solution converge—either by refining the mesh size

Laguerre Matrix-Collocation Method to Solve Systems of Pantograph Type Delay Differential Equations

2020

In this study, an improved matrix method based on collocation points is developed to obtain the approximate solutions of systems of high-order pantograph type delay differential equations with variable coefficients. These kinds of systems described by the existence of linear functional argument play a critical role in defining many different phenomena and particularly, arise in industrial applications and in studies based on biology, economy, electrodynamics, physics and chemistry. The technique we have used reduces the mentioned delay system solution with the initial conditions to the solution of a matrix equation with the unknown Laguerre coefficients. Thereby, the approximate solution is…

A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering

2021

<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…

Valodu centru mājaslapu analīze

2018

Šajā darbā uzmanība tiek veltīta galvenokārt Humanitāro zinātņu fakultātes Lietišķās valodniecības centra (LVC) apakšvietnes satura analīzei. Darba mērķis ir noteikt LVC mājaslapas semantiskos kodolus un pārbaudīt vietnes atslēgvārdu un atslēgu vārdkopu saderību Google meklētājprogrammā. Analīze tika veikta ar moderno Google rīku palīdzību un manuāli atpazīstot pašreizējos atslēgvārdus un atslēgu vārdkopas tīmekļa vietnes lapās. Šis pētījums uzsver semantiskā kodola sagatavošanas nozīmi pirms mājaslapas izstrādāšanas, kā arī to, kā ik pa laikam var pārbaudīt atslēgvārdu un atslēgu vārdkopu saderību (Google atpazīšanu). Empīriskais pētījums tika īstenots izmantojot kvalitatīvo un kvantitatīv…

A mesh less approch based upon Radial basis function Hermite collocation method for predicting the cooling and the freezing times of foods

2005

This work presents a meshless numerical scheme for the solution of time dependent non linear heat transfer problems in terms of a radial basis function Hermite collocation approach. The proposed scheme is applied to foodstuff's samples during freezing process; evaluation of the time evolution of the temperature profile along the sample, as well as at the core, is carried out. The moving phase-change zone is identified in the domain and plotted at several timesteps. The robustness of the proposed scheme is tested by a comparison of the obtained numerical results with those found using a Finite Volume Method and with experimental results.

On ordinary differential equations with interface conditions

1968

Lietvārdu kolokāciju variācijas EUR-Lex korpusa tekstos

2021

Angļu valoda arī šobrīd ir nozīmīga ES institūciju darba valoda, kurā parādās pat dažas unikālas “eiro-angļu valodas” iezīmes. Šajā pētījumā aplūkotas dažas vārdu kopas, kas tai raksturīgas, nosakot Eur-LEX angļu valodas korpusa biežākās lietvārdu kolokācijas. Izmantotās metodes bija salīdzinošā literatūras avotu analīze, kā arī vairāki kvantitatīvi un kvalitatīvi korpusanalīzes paņēmieni. Rezultāti parādīja, ka dažas no šīm lietvārdu kolokācijām veido ES terminoloģiju, kamēr citas iespējams sadalīt tuvu sinonīmu grupās pēc semantiskās nozīmes. Iepriekš zināmas juridiskās angļu valodas iezīmes, piemēram, vārdu pāri, apzīmētāju novietojums pēc lietvārda un arhaiski vietniekvārdi tika novērot…