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Titlebook: Spectral Methods; Fundamentals in Sing Claudio Canuto,M. Youssuff Hussaini,Thomas A. Zang Book 2006 Springer-Verlag Berlin Heidelberg 2006

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Algebraic Systems and Solution Techniques,ral information about time discretizations and Sect. 3.3 and CHQZ3, Chap. 3 for some uses of implicit time discretizations with spectral discretizations in space). We concentrate on linear systems, assuming that nonlinear ones are attacked by standard linearization techniques.
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Introduction,also called the expansion or approximating functions) and the test functions (also known as weight functions). The trial functions, which are linear combinations of suitable trial basis functions, are used to provide the approximate representation of the solution. The test functions are used to ensu
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Theory of Stability and Convergence,blems. Analysis of several nonlinear problems is presented in Chap. 7 and in CHQZ3, Chap. 3. For time-dependent problems, only the discretizations in space are considered. Stability for fully discretized time-dependent problems is discussed in Appendix D by a classical eigenvalue analysis and in Cha
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