You should consult other specialised references. In particular, Alternating Direction Implicit (ADI) methods are the standard means of solving PDE in 2 and 3 dimensions. Title. The resulting algorithms are documented are are easily programmed in C++ or other language.
Numerical Partial Differential Equations: Finite Difference Methods. This is a book that approximates the solution of parabolic, first order hyperbolic and systems of partial differential equations using standard finite difference schemes (FDM). p.cm. This is Volume I of a two-volume set (Volume II deals with Conversation Laws and first-order hyperbolic as well as Elliptic problems.
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— 357 p. — ISBN: 0898716292 Learn how to solve complex differential equations using MATLAB.
It is designed to be used as an introductory graduate text for students in applied mathematics, engineering, and the sciences, and with that in mind, presents the theory of finite difference schemes in a way... Издательство Springer, 1999, -573 pp.
Finally, the book uses von Neumann analysis as a means of proving stability (getting a bit long in the tooth).
The theory and practice of FDM is discussed in detail and numerous practical examples (heat equation, convection-diffusion) in one and two space variables are given. 26.10.2011 19:25; Отредактирован 29.10.2011 00:44; Издательство Springer, 1995, -454 pp. There are more robust methods that use monotone schemes, M-matrices and the maximum principle.
Finite differences. Numerical Partial Differential Equations: Finite Difference Methods . 2. It digs into the nitty-gritty of mapping a PDE to a FDM scheme while taking nasty boundary conditions into consideration. This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. - 832 pages. You can write a book review and share your experiences. The book does not cover topics that are also important: operator splitting (Marchuk/Janenko), non-constant coefficient PDEs, nonlinearities. A unified view of stability... Wiley, 2005. The file will be sent to your Kindle account. 1.1 Example of Problems Leading to Partial Differential Equations. Thomas This is a book that approximates the solution of parabolic, first order hyperbolic and systems of partial differential equations using standard finite difference schemes (FDM).
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