c19-3 (779618), страница 2
Текст из файла (страница 2)
In fact, as a rule of thumb, it is often sufficient to have stable Ui ’sonly for the operator pieces having the highest number of spatial derivatives — theother Ui ’s can be unstable — to make the overall scheme stable!It is at this point that we turn our attention from initial value problems toboundary value problems. These will occupy us for the remainder of the chapter.CITED REFERENCES AND FURTHER READING:Ames, W.F. 1977, Numerical Methods for Partial Differential Equations, 2nd ed. (New York:Academic Press).19.4 Fourier and Cyclic Reduction Methods forBoundary Value ProblemsAs discussed in §19.0, most boundary value problems (elliptic equations, forexample) reduce to solving large sparse linear systems of the formA·u=b(19.4.1)either once, for boundary value equations that are linear, or iteratively, for boundaryvalue equations that are nonlinear.Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use.
Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).might profitably use an explicit scheme for the advective term combined with aCrank-Nicholson or other implicit scheme for the diffusion term.The alternating-direction implicit (ADI) method, equation (19.3.16), is anexample of operator splitting with a slightly different twist.
Let us reinterpret(19.3.19) to have a different meaning: Let U1 now denote an updating method thatincludes algebraically all the pieces of the total operator L, but which is desirablystable only for the L1 piece; likewise U2 , . . . Um . Then a method of getting fromun to un+1 is.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
