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Numerical Solution of Partial Differential Equations
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To be simpler, the idea in this book is more "These are the conditions in which we can develop a numerical scheme, and this is a good numerical scheme to use given the conditions" than it is "This is how we develop a numerical scheme."
Which is a useful topic, but unfortunately if one tried to apply this to, say, a typical program or course in Computational Fluid Dynamics, well, this book can be completely skipped and one can come out of said program or course knowing more about contributing to research in numerical methods (in general, not just with applications to fluid dynamics) than this book could ever provide.
For the person who is fully aware of the nature of some problem and wishes to find some numerical scheme to come up with, say, a quick presentation of efficiency in how said problem's solution accurately reflects a given model or physical data, then this book is pretty good for that, but I'm convinced you can find a better book elsewhere. It just seems too narrow a focus. For that, I agree with the other reviewer who described topics as "ad hoc."
On the other hand, this book is pretty demanding. Presentation is not entirely clear and a strong knowledge of PDEs and analysis (more aligned with mathematical analysis than a typical student's first few semesters in numerical analysis) are largely assumed.Read more ›
It appears to me that this book was written in order to remove all of the rigorous mathematical details of the Richtmyer and Morton book on Finite Difference Methods. I would not use this as a text for any course in numerical PDE. As strange as this may sound, books on CFD tend to do a better job at numerical analysis but a poor job at CFD! I would shop around until you find something you feel comfortable with. This one just doesn't do it for me.