Fornberg B. High-Accuracy Finite Difference Methods 2025 torrent

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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.
Preface.
Introduction to Finite Difference Methods.
Brief Summary of Pseudospectral Methods.
FD Approximations for Ordinary Differential Equations.
Grid-based FD Approximations for Partial Differential Equations.
Mesh-Free FD Approximations.
FD in the Complex Plane.
FD-based Methods for Quadrature and Infinite Sums.
Fractional-Order Derivatives.
Appendix A Polynomial Interpolation.
Appendix B Splines.
Appendix C Fourier Transforms, Fourier Series, and the FFT Algorithm.
Appendix D Lagrange Multipliers.
Appendix E Extrapolation Methods.
Appendix F Trade-off s between Accuracy Orders and Other Approximation Features.
Appendix G Node Sets for FD and RBF-FD-based PDE Discretizations.
References.
Index