000			02256 a2200229 4500
003			OSt
005			20241016152339.0
008			241016b |||||||| |||| 00| 0 eng d
020			_a9780521792110
040			_aICTS-TIFR
050			_aQC20.7.S64
100			_aJan S. Hesthaven
245			_aSpectral methods for time-dependent problems
260			_bCambridge University Press, _aNew York: _c[c2007]
300			_a273 p.
490			_aCambridge Monographs on Applied and Computational Mathematics _v21
505			_a1 - From local to global approximation 2 - Trigonometric polynomial approximation 3 - Fourier spectral methods 4 - Orthogonal polynomials 5 - Polynomial expansions 6 - Polynomial approximation theory for smooth functions 7 - Polynomial spectral methods 8 - Stability of polynomial spectral methods 9 - Spectral methods for nonsmooth problems 10 - Discrete stability and time integration 11 - Computational aspects 12 - Spectral methods on general grids
520			_aSpectral 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. --- summary provided by publisher
700			_aSigal Gottlieb
700			_aDavid Gottlieb
942			_2lcc _cBK
999			_c35125 _d35125