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Thomas J.W. Numerical Partial Differential Equations: Finite Difference Methods. Conservation Laws and Elliptic Equations
Издательство Springer, 1999, -573 pp.

This book is the second part of a two part text on the numerical solution of partial differential equations. Part 1 (TAM 22: Numerical Partial Differential Equations: Finite Difference Methods) is devoted to the basics and includes consistency, stability and convergence results for one and two dimensional parabolic and hyperbolic partial differential equations-both scalar equations and systems of equations. This volume, subtitled Conservation Laws and Elliptic Equations, includes stability results for difference schemes for solving initial-boundary-value problems, analytic and numerical results for both scalar and systems of conservation laws, numerical methods for elliptic equations and an introduction to methods for irregularly shaped regions and for computation problems that need grid refinements. In the Preface to Part 1 (included below), I describe the many ways that I have taught courses out of the material in both Parts 1 and
2. Although I will not repeat those descriptions here, I do emphasize that the two parts of the text are strongly intertwined. Part 1 was used to set up some of the material done in Part 2, and Part 2 uses many results from Part L The contribution that I hope Chapter 8 of Part 2 makes to the subject is to give a description of how to use the Gustafsson-Kreiss-Sundstrom-Osher theory (GKSO theory) to choose numerical boundary conditions when they are necessary. In Chapters 9 and 10 I try to give a reasonably complete coverage of numerical methods for solving conservation laws and elliptic equations. Chapter 11 is meant to introduce the reader to the fact that there are methods for treating irregular regions and for placing refined grids in regions that need them. It is hoped that Parts 1 and 2 help prepare the reader to solve a broad spectrum of problems involving partial differential equations.
In addition to the people I have already thanked in the Preface to Part 1, I would like to thank Ross Heikes who pushed me to include as much as I did in Chapter
9. I would also like to pay tribute to Amiram Harten. His papers, which were readable and of excellent quality, have made a large contribution to the field of the numerical solution of conservation laws. And finally, I would like to thank my family, Ann, David, Michael, Carrie and Susan, for the patience shown when Part 2 took me much longer to write than I predicted. A?, before, the mistakes are mine and I would appreciate it if you should send any mistakes that you find to thomas(собачка)math.colostate.edu. Thank you.
Stability of Initial-Boundary- Value Schemes.
Conservation Laws.
Elliptic Equations.
Irregular Regions and Grids.
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