High-Accuracy Finite Difference Methods

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.

• 1. Introduction to finite difference methods; 2. Brief summary of pseudospectral methods; 3. FD approximations for ordinary differential equations; 4. Grid-based FD approximations for partial differential equations; 5. Mesh-free FD approximations; 6. FD in the complex plane; 7. FD-based methods for quadrature and infinite sums; 8. Fractional-order derivatives; A. Polynomial interpolation; B. Splines; C. Fourier transforms, Fourier series, and the FFT algorithm; D. Lagrange multipliers; E. Extrapolation methods; F. Trade-offs between accuracy orders and other approximation features; G. Node sets for FD and RBF-FD-based PDE discretizations; References; Index.

'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