TY - BOOK ID - 10100218 TI - Spectral methods for time-dependent problems AU - Hesthaven, Jan S. AU - Gottlieb, Sigal AU - Gottlieb, David PY - 2007 SN - 0521792118 9780521792110 9780511618352 9780511261077 0511261071 0511260504 9780511260506 0511618352 1107158621 1280749083 9786610749089 0511259239 0511319924 0511259883 PB - Cambridge : Cambridge University Press, DB - UniCat KW - 519.63 KW - 519.6 KW - 517.95 KW - Numerical methods for solution of partial differential equations KW - Computational mathematics. Numerical analysis. Computer programming KW - Partial differential equations KW - Differential equations, Hyperbolic. KW - Differential equations, Partial. KW - Spectral theory (Mathematics) KW - Spectral theory (Mathematics). KW - 517.95 Partial differential equations KW - 519.6 Computational mathematics. Numerical analysis. Computer programming KW - 519.63 Numerical methods for solution of partial differential equations KW - Differential equations, Hyperbolic KW - Differential equations, Partial KW - Functional analysis KW - Hilbert space KW - Measure theory KW - Transformations (Mathematics) KW - Hyperbolic differential equations UR - https://www.unicat.be/uniCat?func=search&query=sysid:10100218 AB - Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, round-off errors and the formulation of spectral methods on general grids. These will be especially helpful for practitioners. ER -