Time-dependent Partial Differential Equations and Their Numerical Solution - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Time-dependent Partial Differential Equations and Their Numerical Solution write by Heinz-Otto Kreiss. This book was released on 2012-12-06. Time-dependent Partial Differential Equations and Their Numerical Solution available in PDF, EPUB and Kindle. This book studies time-dependent partial differential equations and their numerical solution, developing the analytic and the numerical theory in parallel, and placing special emphasis on the discretization of boundary conditions. The theoretical results are then applied to Newtonian and non-Newtonian flows, two-phase flows and geophysical problems. This book will be a useful introduction to the field for applied mathematicians and graduate students.
Introduction to Numerical Methods for Time Dependent Differential Equations
Introduction to Numerical Methods for Time Dependent Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Numerical Methods for Time Dependent Differential Equations write by Heinz-Otto Kreiss. This book was released on 2014-04-24. Introduction to Numerical Methods for Time Dependent Differential Equations available in PDF, EPUB and Kindle. Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.
Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers
Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers write by Moysey Brio. This book was released on 2010-09-21. Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers available in PDF, EPUB and Kindle. It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations
Finite Difference Methods for Ordinary and Partial Differential Equations
Finite Difference Methods for Ordinary and Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Difference Methods for Ordinary and Partial Differential Equations write by Randall J. LeVeque. This book was released on 2007-01-01. Finite Difference Methods for Ordinary and Partial Differential Equations available in PDF, EPUB and Kindle. This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
High Order Difference Methods for Time Dependent PDE
High Order Difference Methods for Time Dependent PDE - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook High Order Difference Methods for Time Dependent PDE write by Bertil Gustafsson. This book was released on 2007-12-06. High Order Difference Methods for Time Dependent PDE available in PDF, EPUB and Kindle. This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.
