Partial Differential Equations Springer

A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations.

Authors: Bartels, Sören
Matlab implementations illustrate the devised methods
Problems, projects, and quizzes allow for self-evaluation
Includes theoretical and physical backgrounds of mathematical models

The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied.

The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied.

Authors: Hesthaven, Jan S, Rozza, Gianluigi, Stamm, Benjamin
The first book to introduce certified reduced basis methods for parametrized partial differentiation equations
Unique focus on both the mathematical aspects and algorithmic elements of the methods
Essential examples provide a point of departure for the development of more advanced applications

Authors: Jüngel, Ansgar
Provides an easy-to-read overview of entropy methods for diffusive equations
The first book to summarize entropy methods for cross-diffusion systems
The majority of the content should be accessible for advanced undergraduate and graduate students

Editors: Barrenechea, G.R., Brezzi, F., Cangiani, A., Georgoulis, E.H. (Eds.)
The authors are the leading experts in the field. It is hard to find such a selected list of authors writing about the developments they are carrying out at present
The main developments in recent approaches to numerical PDEs are gathered in this book
The survey nature of each contribution makes the volume an ideal reading for practitioners, academics, as well as graduate students wishing to grasp the fundamental aspect of modern numerical PDE approaches

A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution.

This book covers numerical methods for partial differential equations: discretization methods such as finite difference, finite volume and finite element methods; solution methods for linear and nonlinear systems of equations and grid generation.
The book takes account of both the theory and implementation, providing simultaneously both a rigorous and an inductive presentation of the technical details. It contains modern topics such as adaptive methods, multilevel methods and methods for convection-dominated problems. Detailed illustrations and extensive exercises are included.