## Kreiss, Heinz-Otto

# Introduction to Numerical Methods for Time Dependent Differential Equations

**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.

**Keywords:** time, methods, fundamentals, differential, solutions, equations, introduction, dependent, numerical, selfcontained, partial, differential equations, pdes, book, two parts, ordinary, odes, notions, presentation, fundamental, crucial, theory

- Author(s)
- Kreiss, Heinz-Otto
- Ortiz, Omar Eduardo
- Publisher
- John Wiley and Sons, Inc.
- Publication year
- 2014
- Language
- en
- Edition
- 1
- Page amount
- 192 pages
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (ePUB)
- 9781118838914
- Printed ISBN
- 9781118838952