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＜E-Book＞
Numerical Solutions of Partial Differential Equations / by Silvia Bertoluzza, Silvia Falletta, Giovanni Russo, Chi-Wang Shu
(Advanced Courses in Mathematics - CRM Barcelona. ISSN:22970312)

Edition	1st ed. 2009.
Publisher	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
Year	2009
Language	English
Size	X, 202 p : online resource
Authors	*Bertoluzza, Silvia author Falletta, Silvia author Russo, Giovanni author Shu, Chi-Wang author SpringerLink (Online service)
Subjects	LCSH:Numerical analysis LCSH:Differential equations FREE:Numerical Analysis FREE:Differential Equations
Notes	Wavelets and Partial Differential Equations -- What is a Wavelet? -- The Fundamental Property of Wavelets -- Wavelets for Partial Differential Equations -- High-Order Shock-Capturing Schemes for Balance Laws -- Upwind Scheme for Systems -- The Numerical Flux Function -- Nonlinear Reconstruction and High-Order Schemes -- Central Schemes -- Systems with Stiff Source -- Discontinuous Galerkin Methods: General Approach and Stability -- Time Discretization -- Discontinuous Galerkin Method for Conservation Laws -- Discontinuous Galerkin Method for Convection-Diffusion Equations -- Discontinuous Galerkin Method for PDEs Containing Higher-Order Spatial Derivatives 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 HTTP:URL=https://doi.org/10.1007/978-3-7643-8940-6

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