Numerical Solutions of Partial Differential Equations

• Main Authors: Bertoluzza, Silvia (Author), Russo, Giovanni (Author), Falletta, Silvia (Author), Shu, Chi-Wang (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2009.
• Series: Advanced Courses in Mathematics - CRM Barcelona
• Subjects: Mathematics.; Partial differential equations.; Numerical analysis.; Numerical Analysis.; Partial Differential Equations.

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...

Table of Contents:

• 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.