The analysis in this book is presented in a unified framework using the non-uniformly weighted Sobolev spaces which lead to simplified analysis and more precise estimates. The book contains, in particular, efficient spectral algorithms and their error analysis for higher-order differential equations, integral equations, problems in unbounded domains and high-dimensional domains. A set of well structured Matlab codes is available online so the readers can easily modify and expand.

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Spectral Methods Jie Shen, Tao Tang, Li-Lian Wang

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