Partial Differential Equations Modeling, Analysis and Numerical Approximation [Paperback]

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.

 

Foreword.- Mathematical modeling and PDEs.- The finite difference method for elliptic problems.- A review of analysis.- The variational formulation of elliptic PDEs.-Variational approximation methods for elliptic PDEs.- The finite element method in dimension two.- The heat equation.- The finite difference method for the heat equation.- The wave equation.- The finite volume method.- Index.- References.

This textbook covers a broad array of aspects of partial differential equations (PDEs), ranging from a study of their analytical properties to the approximate numerical simulations of their solutions. The level of the book is mainly targeted towards Masters students in applied mathematics or related fields of engineering. & The topics on modeling and approximating partial differential equations are well chosen and are presented in a logical and balanced order. (Michael M. Tung, Mathematical Reviews, June, 2017)

This work explores the field of partial differential equations in an advanced manner. & authlӻ