High-Accuracy Finite Difference Methods

Bengt Fornberg (University of Colorado Boulder)

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English

Cambridge University Press
05 June 2025

Numerical analysis

Series: Cambridge Monographs on Applied and Computational Mathematics

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.

By: Bengt Fornberg (University of Colorado Boulder)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
ISBN: 9781009566537
ISBN 10: 1009566539
Series: Cambridge Monographs on Applied and Computational Mathematics
Pages: 246
Publication Date: 05 June 2025
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Forthcoming

Bengt Fornberg, now Professor Emeritus, joined the University of Colorado Boulder in 1995 following positions at CERN, Caltech, and Exxon Corporate Research. He has authored three previous books, including Volume 1 in this present series 'Cambridge Monographs on Applied and Computational Mathematics.' He is a Guggenheim and a SIAM Fellow.

Reviews for High-Accuracy Finite Difference Methods

'In a journey ranging far wider than the title suggests, Fornberg compels the reader to get fingers on keyboard to explore many areas of modern scientific computing (quadrature, differential equations, complex approximation, fractional derivatives). Written in the author's inimitable 'one-picture-worth-a-thousand-proofs'-style and generously annotated with historical tidbits, this is an enjoyable read from beginning to end.' J. A. C. Weideman, Stellenbosch University 'Fornberg is the expert in high-order finite differencing - nobody else could have written this remarkable book.' Nick Trefethen, Harvard University