Introduction to Numerical Methods for Time Dependent Differential Equations

Heinz-Otto Kreiss, Omar Eduardo Ortiz

ISBN 10: 1118838955 / ISBN 13: 9781118838952

Verlag: John Wiley and Sons Inc, US, 2014

Beschreibung

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 approximationsMultiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equationsA simplified approach in a one space dimensionAnalytical 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.

Bestandsnummer des Verkäufers LU-9781118838952

Bibliografische Details

• Titel: Introduction to Numerical Methods for Time Dependent Differential Equations
• Verlag: John Wiley and Sons Inc, US
• Erscheinungsjahr: 2014
• Sprache: Englisch
• ISBN-10: 1118838955
• ISBN-13: 9781118838952
• Einband: Hardback
• Zustand: New
• Gewicht: 448 Gramm

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

HEINZ-OTTO KREISS, PHD, is Professor Emeritus in the Department of Mathematics at the University of California, Los Angeles and is a renowned mathematician in the field of applied mathematics.

OMAR EDUARDO ORTIZ, PHD, is Professor in the Department of Mathematics, Astronomy, and Physics at the National University of Córdoba, Argentina. Dr. Ortiz’s research interests include analytical and numerical methods for PDEs applied in physics.