Generalized Collocation Methods
Title | Generalized Collocation Methods PDF eBook |
Author | Nicola Bellomo |
Publisher | Springer Science & Business Media |
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.
Generalized Collocation Method and Its Particular Cases and Comparative Analysis
Title | Generalized Collocation Method and Its Particular Cases and Comparative Analysis PDF eBook |
Author | Paul Shuleshko |
Publisher | |
Pages | 76 |
Release | 1960 |
Genre | Differential equations |
ISBN |
Collocation and Galerkin Time-Stepping Methods
Title | Collocation and Galerkin Time-Stepping Methods PDF eBook |
Author | H. T. Huynh |
Publisher | BiblioGov |
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.
Trefftz and Collocation Methods
Title | Trefftz and Collocation Methods PDF eBook |
Author | Z-C. Li |
Publisher | WIT Press |
Pages | 433 |
Release | 2008-02-22 |
Genre | Technology & Engineering |
ISBN | 1845641531 |
This title was reviewed in the January 2009 issue of Mathematical Reviews.
Collocation Methods for Volterra Integral and Related Functional Differential Equations
Title | Collocation Methods for Volterra Integral and Related Functional Differential Equations PDF eBook |
Author | Hermann Brunner |
Publisher | Cambridge University Press |
Pages | 620 |
Release | 2004-11-15 |
Genre | Mathematics |
ISBN | 9780521806152 |
Publisher Description
Generalized Multipole Techniques for Electromagnetic and Light Scattering
Title | Generalized Multipole Techniques for Electromagnetic and Light Scattering PDF eBook |
Author | T. Wriedt |
Publisher | Elsevier |
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.
Collocation and Galerkin Time-Stepping Methods
Title | Collocation and Galerkin Time-Stepping Methods PDF eBook |
Author | National Aeronautics and Space Adm Nasa |
Publisher | Independently Published |
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