Author: W. E. SchiesserPublisher:
ISBN:
Category :
Languages : en
Pages : 63
Book Description
Numerical Method of Lines Integration of Partial Differential Equations in Two Dimensions
Author: W. E. SchiesserNumerical Method of Lines Integration of Partial Differential Equations in Three Dimensions
Author: W. E. SchiesserPublisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 62
Book Description
Numerical Methods for Partial Differential Equations
Author: William F. AmesPublisher: Academic Press
ISBN: 1483262421
Category : Mathematics
Languages : en
Pages : 380
Book Description
Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.
Differential Systems Simulator, version 2
Author: W. E. SchiesserNumerical Analysis of Partial Differential Equations Using Maple and MATLAB
Author: Martin J. GanderPublisher: SIAM
ISBN: 161197531X
Category : Science
Languages : en
Pages : 163
Book Description
This book provides an elementary yet comprehensive introduction to the numerical solution of partial differential equations (PDEs). Used to model important phenomena, such as the heating of apartments and the behavior of electromagnetic waves, these equations have applications in engineering and the life sciences, and most can only be solved approximately using computers.? Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB? code for each of the discretization methods and exercises. It also gives self-contained convergence proofs for each method using the tools and techniques required for the general convergence analysis but adapted to the simplest setting to keep the presentation clear and complete. This book is intended for advanced undergraduate and early graduate students in numerical analysis and scientific computing and researchers in related fields. It is appropriate for a course on numerical methods for partial differential equations.
Numerical Solution of Partial Differential Equations in Science and Engineering
Author: Leon LapidusPublisher: John Wiley & Sons
ISBN: 1118031210
Category : Mathematics
Languages : en
Pages : 677
Book Description
From the reviews of Numerical Solution of PartialDifferential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, evenexhaustive, survey of the subject . . . [It] is unique in that itcovers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic)mode of presentation. Many different computational schemes aredescribed in great detail . . . Numerous practical examples andapplications are described from beginning to the end, often withcalculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages tolucid developments of the methods [for solving partial differentialequations] . . . the writing is very polished and I found it apleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen andEli L. Isaacson. A modern, practical look at numerical analysis,this book guides readers through a broad selection of numericalmethods, implementation, and basic theoretical results, with anemphasis on methods used in scientific computation involvingdifferential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan.Presenting an easily accessible treatment of mathematical methodsfor scientists and engineers, this acclaimed work covers fluidmechanics and calculus of variations as well as more modernmethods-dimensional analysis and scaling, nonlinear wavepropagation, bifurcation, and singular perturbation. 1996(0-471-16513-1) 496 pp.
Partial Differential Equations
Author: Walter A. StraussPublisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
The Numerical Method of Lines
Author: William E. SchiesserPublisher: Elsevier
ISBN: 0128015519
Category : Mathematics
Languages : en
Pages : 341
Book Description
This is the first book on the numerical method of lines, a relatively new method for solving partial differential equations. The Numerical Method of Lines is also the first book to accommodate all major classes of partial differential equations. This is essentially an applications book for computer scientists. The author will separately offer a disk of FORTRAN 77 programs with 250 specific applications, ranging from "Shuttle Launch Simulation" to "Temperature Control of a Nuclear Fuel Rod."
Finite Difference Methods for Ordinary and Partial Differential Equations
Author: Randall J. LeVequePublisher: SIAM
ISBN: 9780898717839
Category : Mathematics
Languages : en
Pages : 356
Book Description
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.
A Method Of Lines In The Numerical Solution Of Schrödinger Equation
Author: Lawal Sa'aduPublisher: LAP Lambert Academic Publishing
ISBN: 9783659292354
Category : Differential equations, Partial
Languages : en
Pages : 144
Book Description
The Method of Lines (MOL) has been one of the simplest but effective technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. This work describes numerical solution of 1-dimensional Schrodinger equation using the method of lines approach (MOL) where spatial dimensions were discretized using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting system of initial value problems. The effect of changing the discretization size on the accuracy of the solution procedure versus changing the step size in the integration of the resulting differential equation was also studied with the incorporation of Simpson's rule function in MATLAB.