Silvia Bertoluzza & Silvia Falletta 
Numerical Solutions of Partial Differential Equations [PDF ebook] 

This book presents some of the latest developments in numerical analysis and scientific computing. Specifically, it covers central schemes, error estimates for discontinuous Galerkin methods, and the use of wavelets in scientific computing.

Mục lục

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.