Implementing Spectral Methods for Partial Differential Equations : Algorithms for Scientists and Engineers

Beschreibung:

Neuware - This book offers a systematic and self-contained approach to solvepartial differential equations numerically using single and multidomain spectralmethods. It contains detailed algorithms in pseudocode for the applicationof spectral approximations to both one and two dimensional PDEsof mathematical physics describing potentials,transport, and wave propagation. David Kopriva, a well-known researcherin the field with extensive practical experience, shows how only a fewfundamental algorithms form the building blocks of any spectral code, evenfor problems with complex geometries. The book addresses computationaland applications scientists, as it emphasizes thepractical derivation and implementation of spectral methods over abstract mathematics. It is divided into two parts: First comes a primer on spectralapproximation and the basic algorithms, including FFT algorithms, Gaussquadrature algorithms, and how to approximate derivatives. The secondpart shows how to use those algorithms to solve steady and time dependent PDEs in one and two space dimensions. Exercises and questions at theend of each chapter encourage the reader to experiment with thealgorithms. Bestandsnummer des Verkäufers 9789048122608

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Über die Autorin bzw. den Autor:

David Kopriva is Professor of Mathematics at the Florida State University, where he has taught since 1985. He is an expert in the development, implementation and application of high order spectral multi-domain methods for time dependent problems. In 1986 he developed the first multi-domain spectral method for hyperbolic systems, which was applied to the Euler equations of gas dynamics.