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Titlebook: Numerical Solutions of Partial Differential Equations; Silvia Bertoluzza,Giovanni Russo,Chi-Wang Shu Textbook 2009 Birkhäuser Basel 2009 d

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发表于 2025-3-21 17:30:48 | 显示全部楼层 |阅读模式
书目名称Numerical Solutions of Partial Differential Equations
编辑Silvia Bertoluzza,Giovanni Russo,Chi-Wang Shu
视频video
概述The review on central schemes, on error estimates for discontinuous Galerkin methods and on the use of wavelets in scientific computing form an excellent teaching material for graduate students.Includ
丛书名称Advanced Courses in Mathematics - CRM Barcelona
图书封面Titlebook: Numerical Solutions of Partial Differential Equations;  Silvia Bertoluzza,Giovanni Russo,Chi-Wang Shu Textbook 2009 Birkhäuser Basel 2009 d
描述.This volume offers researchers the opportunity to catch up with important developments in the field of numerical analysis and scientific computing and to get in touch with state-of-the-art numerical techniques. ..The book has three parts. The first one is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of writing equivalent norms for the scale of Besov spaces allows to develop some new methods. The second part provides an overview of the modern finite-volume and finite-difference shock-capturing schemes for systems of conservation and balance laws, with emphasis on providing a unified view of such schemes by identifying the essential aspects of their construction. In the last part a general introduction is given to the discontinuous Galerkin methods for solving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates..
出版日期Textbook 2009
关键词differential equation; numerical analysis; partial differential equation; scientific computing; wavelet;
版次1
doihttps://doi.org/10.1007/978-3-7643-8940-6
isbn_softcover978-3-7643-8939-0
isbn_ebook978-3-7643-8940-6Series ISSN 2297-0304 Series E-ISSN 2297-0312
issn_series 2297-0304
copyrightBirkhäuser Basel 2009
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What is a Wavelet?trict ones (a wavelet is the dilated and translated version of a . satisfying a suitable set of properties) to more and more general definitions. The aim of this chapter is to review the classical definition of wavelets for R and then point out which of its properties can be retained when replacing
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Wavelets for Partial Differential Equationss we will see how we can take advantage of such a property in the design of new efficient methods for the solution of PDEs. Let us assume from now on that we have a couple of multiresolution analyses . and . satisfying all space and frequency localization assumptions of Section 2.2.
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Central Schemestion, which is necessary to define the flux across the cell edges. In the Godunov representation of the solution, in fact the function .(.) is piecewise smooth (in general, piecewise polynomial), with discontinuities at cell boundaries.
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Systems with Stiff Sourcerder 1 to very small values if compared to the time scale determined by the characteristic speeds of the system. In this second case the hyperbolic system with relaxation is said to be stiff, and typically its solutions are well approximated by solutions of a suitably reduced set of conservation law
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f the world. It has proven effectiveness as it has significant effect on culture, environment and provide economic incentive both in developed regions and in developing or poor regions. This paper aims to explain the relationship between tourism activities and the economic development, and to measur
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