Partial Differential Equations with Numerical Methods

by Stig Larsson, Vidar Thomée

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Genres: Mathematics

272 pages, Paperback

First published March 9, 2005

Reviews

[Per Ljung · Rating 5 out of 5]

Starts from the ground up and provides the very essentials in an interesting and pedagogical way. I am particularly fond of the parts on time-dependent equations (for the interested reader, Thomée’s ”Galerkin Finite Element Methods for Parabolic Problems” provides an exceptional in-depth discussion on the topic). I have revisited, and will revisit, this gem plenty times more.

[Mohammad Zakerzadeh · Rating 4 out of 5]

Really good to start! It is comprehensive while not too long. It covers the basic theorems and lemmas of elliptic, parabolic and hyperbolic PDEs. Just short proofs are presented and this helps the beginner reader not to put it aside.

It includes FD and FE methods for each of three types. Also there are some special chapters cover the analytical tools in deep, like eigenvalue problems.

Typos are more than acceptable, e.g. in version 2005, "continuous embedding theorem" in the Appendix A is presented in the opposite direction!

The author made an errata in his personal website, advise you to see that!

[Joe Cole · Rating 5 out of 5]

Good discuss for partial differential equations theory. The book discusses the essential equations and methods with both clarity and rigor.