Generalized Collocation Methods
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Author | : Nicola Bellomo |
Publisher | : Springer Science & Business Media |
Total Pages | : 206 |
Release | : 2007-09-26 |
Genre | : Mathematics |
ISBN | : 0817646108 |
Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important topic by focusing on collocation methods for solving nonlinear evolution equations and applying them to a variety of mathematical problems. These include wave motion models, hydrodynamic models of vehicular traffic flow, convection-diffusion models, reaction-diffusion models, and population dynamics models. The book may be used as a textbook for graduate courses on collocation methods, nonlinear modeling, and nonlinear differential equations. Examples and exercises are included in every chapter.
Author | : Paul Shuleshko |
Publisher | : |
Total Pages | : 76 |
Release | : 1960 |
Genre | : Differential equations |
ISBN | : |
Author | : H. T. Huynh |
Publisher | : BiblioGov |
Total Pages | : 42 |
Release | : 2013-06 |
Genre | : |
ISBN | : 9781289031084 |
We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods.
Author | : Z-C. Li |
Publisher | : WIT Press |
Total Pages | : 433 |
Release | : 2008-02-22 |
Genre | : Technology & Engineering |
ISBN | : 1845641531 |
This title was reviewed in the January 2009 issue of Mathematical Reviews.
Author | : T. Wriedt |
Publisher | : Elsevier |
Total Pages | : 273 |
Release | : 1999-12-01 |
Genre | : Technology & Engineering |
ISBN | : 0080532373 |
This book is an edited volume of nine papers covering the different variants of the generalized multipole techniques (GMT). The papers were presented at the recent 3rd Workshop on Electromagnetics and Light Scattering - Theory and Applications, which focused on current GMT methods. These include the multiple multipole method (MMP), the discrete sources method (DSM), Yasuura's method, method of auxiliary sources and null-field method with discrete sources. Each paper presents a full theoretical description as well as some applications of the method in electrical engineering and optics. It also includes both 2D and 3D methods and other applications developed in the former Soviet Union and Japan.
Author | : National Aeronautics and Space Adm Nasa |
Publisher | : Independently Published |
Total Pages | : 40 |
Release | : 2019-01-13 |
Genre | : Science |
ISBN | : 9781793962157 |
We study the numerical solutions of ordinary differential equations by one-step methods where the solution at tn is known and that at t(sub n+1) is to be calculated. The approaches employed are collocation, continuous Galerkin (CG) and discontinuous Galerkin (DG). Relations among these three approaches are established. A quadrature formula using s evaluation points is employed for the Galerkin formulations. We show that with such a quadrature, the CG method is identical to the collocation method using quadrature points as collocation points. Furthermore, if the quadrature formula is the right Radau one (including t(sub n+1)), then the DG and CG methods also become identical, and they reduce to the Radau IIA collocation method. In addition, we present a generalization of DG that yields a method identical to CG and collocation with arbitrary collocation points. Thus, the collocation, CG, and generalized DG methods are equivalent, and the latter two methods can be formulated using the differential instead of integral equation. Finally, all schemes discussed can be cast as s-stage implicit Runge-Kutta methods. Huynh, H. T. Glenn Research Center NASA/TM-2011-216340, E-17277
Author | : Jan S. Hesthaven |
Publisher | : Springer Science & Business Media |
Total Pages | : 507 |
Release | : 2010-10-29 |
Genre | : Mathematics |
ISBN | : 3642153372 |
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.
Author | : Wen Chen |
Publisher | : Springer Science & Business Media |
Total Pages | : 98 |
Release | : 2013-11-09 |
Genre | : Technology & Engineering |
ISBN | : 3642395724 |
This book surveys the latest advances in radial basis function (RBF) meshless collocation methods which emphasis on recent novel kernel RBFs and new numerical schemes for solving partial differential equations. The RBF collocation methods are inherently free of integration and mesh, and avoid tedious mesh generation involved in standard finite element and boundary element methods. This book focuses primarily on the numerical algorithms, engineering applications, and highlights a large class of novel boundary-type RBF meshless collocation methods. These methods have shown a clear edge over the traditional numerical techniques especially for problems involving infinite domain, moving boundary, thin-walled structures, and inverse problems. Due to the rapid development in RBF meshless collocation methods, there is a need to summarize all these new materials so that they are available to scientists, engineers, and graduate students who are interest to apply these newly developed methods for solving real world’s problems. This book is intended to meet this need. Prof. Wen Chen and Dr. Zhuo-Jia Fu work at Hohai University. Prof. C.S. Chen works at the University of Southern Mississippi.
Author | : N. Bellomo |
Publisher | : |
Total Pages | : 30 |
Release | : 1999 |
Genre | : |
ISBN | : |
Author | : J.jr. Douglas |
Publisher | : Springer |
Total Pages | : 152 |
Release | : 2006-08-01 |
Genre | : Mathematics |
ISBN | : 3540383379 |