Advanced search
Publication Cover
Inverse Problems in Science and Engineering Volume 17, 2009 - Issue 7
Submit an article Journal homepage
196
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

An alternating boundary integral based method for a Cauchy problem for the Laplace equation in a quadrant

Roman ChapkoFaculty of Applied Mathematics and Computer Science, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine
&
B. Tomas JohanssonSchool of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
Pages 871-883 | Received 18 Sep 2008, Accepted 21 Nov 2008, Published online: 16 Sep 2009

References

  • Calderón, A-P, 1958. Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), pp. 16–36.
  • Carleman, T, 1939. Sur un problème d'unicité pur les systèmes d'équations aux dérivées partielles à deux variables indépendantes, (French), Ark. Mat., Astr. Fys. 26 (1939), pp. 1–9.
  • Kozlov, VA, and Maz'ya, VG, 1989. On iterative procedures for solving ill-posed boundary value problems that preserve differential equations, Algebra i Analiz 1 (1989), pp. 144–170, (English transl.: Leningrad Math. J. 1 (1990), pp. 1207–1228).
  • Chapko, R, and Johansson, BT, 2008. An alternating boundary integral based method for a Cauchy problem for Laplace equation in semi-infinite domains, Inverse Probl. Imaging 3 (2008), pp. 317–333.
  • Bastay, G, Johansson, T, Kozlov, V, and Lesnic, D, 2006. An alternating method for the stationary Stokes system, ZAMM 86 (2006), pp. 268–280.
  • Baumeister, J, and Leitão, A, 2001. On iterative methods for solving ill-posed problems modeled by partial differential equations, J. Inv. Ill-Posed Probl. 9 (2001), pp. 13–29.
  • Engl, HW, and Leitão, A, 2001. A Mann iterative regularization method for elliptic Cauchy problems, Numer. Funct. Anal. Optim. 22 (2001), pp. 861–884.
  • Jourhmane, M, and Nachaoui, A, 1999. An alternating method for an inverse Cauchy problem, Numer. Algorithms 21 (1999), pp. 247–260.
  • Lesnic, D, Elliott, L, and Ingham, DB, 1997. An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation, Eng. Anal. Bound. Elem. 20 (1997), pp. 123–133.
  • Kozlov, VA, Maz'ya, VG, and Fomin, AV, 1991. An iterative method for solving the Cauchy problem for elliptic equations, Zh. Vychisl. Mat. i Mat. Fiz. 31 (1991), pp. 64–74, (English transl.: USSR Comput. Maths. Math. Phys. 31 (1991), pp. 45–52.
  • Givoli, G, Patlashenko, I, and Keller, JB, 1997. High-order boundary conditions and finite elements for infinite domains, Comput. Meth. Appl. Mech. Eng. 143 (1997), pp. 13–39.
  • Vainikko, GM, and Veretennikov, AY, 1986. Iteration Procedures in Ill-Posed Problems. Moscow: Nauka Publ.; 1986, (in Russian).
  • Jawson, MA, and Symm, G, 1977. Integral Equations Methods in Potential Theory and Elastostatics. London: Academic Press; 1977.
  • Chapko, R, and Kress, R, 1993. "On a Quadrature Method for a Logarithmic Integral Equation of the First Kind". In: Agarwal, RP, ed. World Scientific Series in Applicable Analysis. Vol. 2. Singapore: Contributions in Numerical Mathematics. World Scientific; 1993. pp. 127–140.
  • Kress, R, 1999. Linear Integral Equations. Heidelberg: Springer-Verlag; 1999.
  • Stenger, F, 1993. Numerical Methods Based on Sinc and Analytic Functions. Heidelberg: Springer-Verlag; 1993.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.