High-accuracy finite difference methods / Bengt Fornberg, University of Colorado Boulder.

Format:

Book

Author/Creator:

Fornberg, Bengt, author.

Series:

Cambridge monographs on applied and computational mathematics ; 42.

Cambridge monographs on applied and computational mathematics ; 42

Language:

English

Subjects (All):

Difference equations.

Physical Description:

1 online resource (xiii, 232 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2025.

Summary:

Scientific computing plays a critically important role in almost all areas of engineering, modeling, and forecasting. The method of finite differences (FD) is a classical tool that is still rapidly evolving, with several key developments barely yet in the literature. Other key aspects of the method, in particular those to do with computations that require high accuracy, often 'fall through the cracks' in many treatises. Bengt Fornberg addresses that failing in this book, which adopts a practical perspective right across the field and is aimed at graduate students, scientists, and educators seeking a follow-up to more typical curriculum-oriented textbooks. The coverage extends from generating FD formulas and applying them to solving ordinary and partial differential equations, to numerical integration, evaluation of infinite sums, approximation of fractional derivatives, and computations in the complex plane.

Contents:

Introduction to finite difference methods

A few historical notes

Finite difference formulas

Errors when applying FD formulas.

Notes:

Title from publisher's bibliographic system (viewed on 16 May 2025).

Description based on publisher supplied metadata and other sources.

ISBN:

1-009-56651-2

1-009-56654-7

OCLC:

1521234862