Partial Differential Equations: Modeling, Analysis and Numerical Approximation

“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 Master’s 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. … authors provide remarks that help clarify and expand on information that was proved. This is a useful feature for the student trying to make connections with the material. … the authors not only provide a brief summary of the material just covered, but also allude to how this material will be seen in the following chapters. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (S. L. Sullivan, Choice, Vol. 54 (9), May, 2017)“This book presents both a theoretical and a numerical approach to partial differential equations. … The book appeals to graduate students as well as to researchers in any field of pure and applied mathematics who want to be introduced to numerical approximation method for PDEs through a rigorous approach.” (Marius Ghergu, zbMATH 1339.35005, 2016)

• 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.