ISSN:
0749-159X
Schlagwort(e):
Mathematics and Statistics
;
Numerical Methods
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Mathematik
Notizen:
In this article, we give a simple method for deriving finite difference schemes on a uniform cubic grid. We consider a general, three-dimensional, second-order, linear, elliptic partial differential equation with variable coefficients. We derive two simple fourth-order schemes. When the coefficients of the second-order mixed derivatives are equal to zero, the fourth-order scheme requires only 19 grid points. When the coefficients of the mixed derivatives are not equal to zero and the coefficients of Uxx, Uyy, and Uzz are equal, we require the 27 points of the cubic grid. Numerical examples are given to demonstrate the performance of the two schemes derived. There does not exist a fourth-order scheme involving 27 grid points for the general case.
Zusätzliches Material:
1 Ill.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1002/num.1690030307
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