Customer Reviews

Computational Partial Differential Equations (Lecture Notes in Computational Science and Engineering)

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In a way, the book is a throwback to a time when most people learning Fortran were not computer programmers per se, but scientists and engineers who needed to solve some problem using computers. In Langtangen's book, the language of choice is C++. A good choice, given that this edition came out in 2003. C++ has one main advantage over Fortran, in its object oriented ability. The procedural aspect of Fortran has trouble scaling to very large code bodies. However, Langtangen is quick to point out that if you take the time to learn C++ via the book, the coding experience is easily transferred to other languages like Java or even Fortran.

He directs the book towards a student or professional in the sciences or engineering, who has to solve a slew of Partial Differential Equations (PDEs). Often, the equations and boundary conditions mean that numerical analysis is required; analytic solutions are rare. The PDEs might be non-linear, which is another source of complexity and possible instability.

Finite element methods take up a large chunk of the text. The discussion is not restricted to the simple case where the space is divided into an equally spaced grid. He considers cases where you might need variable spacing; with a high concentration of grid points in regions of key interest. For example, think of solving for an electromagnetic field or fluid flow field, around a boundary of high curvature.

For linear systems, there is a foray into solving large matrix equations, where the matrices are sparse. Enough theory is developed to make the algorithms plausible.

Be aware that learning C++ thru this book won't give you all that C++ can do. Specifically, the string manipulations are little needed here. True of most computationally intensive code. But if you are not professionally a programmer, then this relative lack should not be a problem.

I highly recommend this author and his texts. The book combines theory, algorithm, pseudo-coding, and working code into an actual intelligible format which is very rare. If you are looking to create real working scientific code this is a must.