Numerical Solutions of Partial Differential Equations

• 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.

From the reviews: "It includes an extended version of the lectures given by the four authors at the Advanced School on Numerical Solutions of Partial Differential Equations: New Trends and Applications, held at the CRM - Barcelona between November 15 - 22, 2007. ... The book is addressed to masterands, for PhD candidates and to research workers in the fields of applied mathematics and engineering." (Constantin I. Popovici, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010) "The book is well written and organized at a difficulty level that precisely meets the target audiences' needs. ... PhD students as well as engineers and researchers in the field of applied mathematics or scientific computing and interested graduate students will find this book an excellent resource to rapid introduction into the field of modern numerical methods ... . serve as a textbook for graduate - level courses in numerical methods ... . be useful for experienced researchers and practitioners both from academia or industry." (Andrzej Myslinski, Control and Cybernetics, Vol. 39 (3), 2010)