Read more
Finite differences are widely used for solving problems in scientific computing. One aspect underrepresented in textbooks concerns high-accuracy methods. Bengt Fornberg addresses that here. Full of conceptual insights, general perspectives, and practical considerations, it will be welcomed by graduate students, researchers, and educators.
List of contents
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.
About the author
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.
