41
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Numerical solution of laplace's equation on non-simply connected regions on R2

&
Pages 253-267 | Received 15 Mar 2000, Published online: 19 Mar 2007

References

  • Günter , N. 1967 . Potential Theory , New York : Ungar Publishing .
  • Kellogg , O.D. 1929 . Foundation of Potential Theory , New York : reprinted by Dover Publications .
  • Mikhlin , S.G. 1966 . Integral Equations , 2nd edn. , London : A.H.Armstrong, Pergamon Press . trans.by
  • Muskhelishvili , N.I. 1946 . Singular Integral Equations , Noordhoff .
  • Pogorzelski , W. 1966 . Integral Equations and Their Applications , London : Pergamon Press .
  • Atkinson , K.E. 1976 . A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind , SIAM .
  • Atkinson , K.E. 1980 . “ The numerical solution of Laplace's equation in three dimension- II ” . In Numerical Treatment of Integral Equations , Edited by: Albertcht , J. and L , Collatz . 1 – 23 . Basel : Birkhauser Verlag .
  • Atkinson , K.E. 1982 . The numerical solution of Laplace's equation in three dimension . SIAM, J.Numer.Anal. , 19 ( 2 )
  • Baker , C. 1977 . The Numerical Treatment of Integral Equations , Oxford Press .
  • Jaswon , M.A. and Symm , G.T. 1977 . Integral Equation Methods in Potential Theory and Elastostatics , London : Academic press .
  • Mc Lean , W. 1985 . “ Boundary Integral Method for Laplace Equation ” . In Thesis , Camberra : Australian National University .
  • Wendland , W.L. 1983 . “ Boundary element methods and their asymptotic convergence ” . In Theoretical Acoustics and Numerical Techniques , Edited by: Filippi , P. Berlin : Springer-Verlag . CISM Courses and Lectures No.277, International Center for Mechanical Sciences.
  • Mayo , A. 1986 . Rapid methods for the conformal mapping of multiply connected region . J.of Comp.and Appl.Math. , 14 : 143 – 153 .
  • Atkinson , K.E. 1997 . The Numerical Solution of Integral Equations of the Second Kind , Cambridge University Press .
  • Anselone , P.M. 1971 . Collectively Compact Operator Approximation Theory and Applications to Integral Equations , Prentice-Hall, Inc .
  • Saavedra , J. 1988 . “ Numerical Solution for Laplace's Equation on a Non-simply Connected Regions ” . In Thesis , The University of Iowa .
  • Davis , P.J. 1959 . “ On the numerical integration of periodic analytic functions ” . In Num.Approx. , Edited by: Ranger , R.E. 45 – 59 . Madison : Univ.of Wisconsin Press .
  • Kantorovic , L. and Krylov , V. 1966 . Approximate Method of Higher Analysis , Groningen , The Netherlands : Intercience Pub.Noordhoff .
  • Miller , C . May 1979 . “ Numerical solution of Two-dimensional Potential Theory Problem Using Integral Equations techniques ” . In Thesis , May , The University of Iowa .
  • Flores , J.D. 1993 . The conjugate gradient method for solving Fredholm integral equations of second kind . Intern.J.Comp.Math. , 48 May : 77 – 94 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.