Partial Differential Equations and Numerical Methods (Reprint Edition) 19 (Series of Famous Mathematical Works Abroad)

Author: (Swedish) Stig Larsson et al.
Publisher:
Publish Date: 2006-05-26
Features: Stig Larsson, the author of "Partial Differential Equations and Numerical Methods," is currently a professor at the Department of Mathematics, Chalmers University of Technology, Sweden, and a member of the Royal Swedish Academy of Sciences. This book combines the mathematical analysis of differential equations with finite difference theory and finite element methods, presenting the fundamental theory of linear partial differential equations and their common numerical solution methods. It elaborates on elliptic, parabolic, and hyperbolic partial differential equations in three chapters each, one chapter on mathematical theory, one on finite difference methods, and one on finite element methods. Before discussing elliptic equations, it covers the two-point boundary value problems of ordinary differential equations; similarly, before discussing parabolic and hyperbolic development problems, it covers the initial value problems of ordinary differential equations. Additionally, there is a chapter on elliptic eigenvalue problems and the expansion of eigenfunctions. The appendix provides the background knowledge of linear functional analysis and Sobolev spaces required for reading this book. No advanced knowledge of mathematical analysis and functional analysis is needed to read this book. It is suitable for senior undergraduate and early graduate students in applied mathematics and engineering.