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A note on the approximation of mildly nonlinear Dirichlet problems by finite differences (1979)

Meyer-Spasche, Rita

Springer

Numerische Mathematik 33 (1979), S. 303-313

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ISSN: 0945-3245

Keywords: AMS(MOS): 65N20 ; CR: 5.17

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary In [9], Simpson proved some theorems concerning the approximation of mildly nonlinear Dirichlet problems −Δu=f (x, u) inD, u=0 on ∂D by finite differences. The assumptionsf(x, 0)≧0 andf u(x, u)〉0 in [9] have turned out to be unnecessarily restrictive and are eliminated in this paper. On the other hand, we considered it necessary to make the smoothness conditions forD slightly more stringent irrespective of the conditions imposed onf.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01398646

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