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  • CR: 5.17  (2)
  • Springer  (2)
  • Nature Publishing Group
  • Oxford University Press
  • Springer Nature
  • 1975-1979  (2)
  • 1970-1974
  • 1960-1964
  • 1935-1939
Collection
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Publisher
  • Springer  (2)
  • Nature Publishing Group
  • Oxford University Press
  • Springer Nature
Years
  • 1975-1979  (2)
  • 1970-1974
  • 1960-1964
  • 1935-1939
  • 1980-1984  (1)
Year
  • 1
    Electronic Resource
    Electronic Resource
    The method of lines for Poisson's equation with nonlinear or free boundary conditions (1978)
    Springer
    Numerische Mathematik 29 (1978), S. 329-344 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The method of lines is used to solve Poisson's equation on an irregular domain with nonlinear or free boundary conditions. The partial differential equation is approximated by a system of second order ordinary differential equations subject to multi-point boundary conditions. The system is solved with an SOR iteration which employs invariant imbedding for each one dimensional problem. An application of the method to a boundary control problem and to a free surface problem arising in electrochemical machining is described. Finally, some theoretical convergence results are presented for a model problem with radiative boundary conditions on fixed boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389216
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  • 2
    Electronic Resource
    Electronic Resource
    A note on the approximation of mildly nonlinear Dirichlet problems by finite differences (1979)
    Springer
    Numerische Mathematik 33 (1979), S. 303-313 
    Details
    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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    Paper (German National Licenses)
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