Collocation Methods for Volterra Integral and Related Functional Differential Equations
Title: Collocation Methods for Volterra Integral and Related Functional Differential Equations | Author(s): Hermann Brunner | Publisher: Cambridge University Press | Year: 2004 | Language: English | Pages : 612 | Size: 29 MB | Extension: pdf
Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena. The present book introduces the reader to the general principles underlying these methods and then describes in detail their convergence properties when applied to ordinary differential equations, functional equations with (Volterra type) memory…
Spline collocation methods for partial differential equations : with applications in R
Title: Spline collocation methods for partial differential equations : with applications in R | Author(s): Schiesser, W. E | Publisher: John Wiley & Sons | Year: 2017 | Language: English | Pages : 552 | Size: 5 MB | Extension: pdf
A comprehensive approach to numerical partial differential equations
Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive…
Generalized Collocation Methods: Solutions to Nonlinear Problems
Title: Generalized Collocation Methods: Solutions to Nonlinear Problems | Author(s): Nicola Bellomo, Bertrand Lods, Roberto Revelli, Luca Ridolfi | Publisher: Birkhäuser | Year: 2007 | Language: English | Pages : 205 | Size: 7 MB | Extension: pdf
This book examines various mathematical tools—based on generalized collocation methods—to solve nonlinear problems related to partial differential and integro-differential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and pollution.
Based on a unified approach combining modeling, mathematical methods, and scientific computation, each chapter begins with several examples…
Trefftz and Collocation Methods
Title: Trefftz and Collocation Methods | Author(s): Z.-C. Li, T.-T. Lu, H-Y. Hu, A. H.-D. Cheng | Publisher: WIT Press | Year: 2008 | Language: English | Pages : 433 | Size: 3 MB | Extension: pdf
This book covers a class of numerical methods that are generally referred to as Collocation Methods. Different from the Finite Element and the Finite Difference Method, the discretization and approximation of the collocation method is based on a set of unstructured points in space. This meshless feature is attractive because it eliminates the bookkeeping requirements of the element based methods. This text discusses several types of collocation methods including the radial basis function method, the Trefftz method, the Schwartz alternating method, and the couple…