High-Accuracy Finite Difference Methods

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.

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.