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Numerical solution of parabolic Cauchy problems in planar corner domains
Ivan Franko National University of Lviv, Ukraine .
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology. EAS, Aston University, Birmingham, UK.
Ivan Franko National University of Lviv, Ukraine .
2014 (English)In: Mathematics and Computers in Simulation, ISSN 0378-4754, Vol. 101, 1-12 p.Article in journal (Refereed) Published
Abstract [en]

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nystrom method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach.

Place, publisher, year, edition, pages
Elsevier , 2014. Vol. 101, 1-12 p.
Keyword [en]
Heat equation; Cauchy problem; Landweber method; Corner singularities; Boundary integral equation
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-108155DOI: 10.1016/j.matcom.2014.03.001ISI: 000336693800001OAI: diva2:729657
Available from: 2014-06-26 Created: 2014-06-26 Last updated: 2014-06-26

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