Partial Differential Equations: Modeling, Analysis and Numerical Approximation
Le Dret, Hervé, Lucquin, Brigitte, "Partial Differential Equations: Modeling, Analysis and Numerical Approximation"
English | 2016 | ISBN-10: 3319270656 | 395 pages | EPUB | 9 MB
English | 2016 | ISBN-10: 3319270656 | 395 pages | EPUB | 9 MB
Covers the whole spectrum of partial differential equations, from modeling, analysis, to numerical analysis with numerical illustrations
Covers the major deterministic numerical methods used in scientific computing practice
Mathematically self-contained
This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.