Mifodijus Sapagovas, Jurij Novickij, Regimantas Ciupaila
Abstract:
We consider an efficient finite difference method solving of two-dimensional
parabolic equations with nonlocal conditions.
The specific feature of the investigated problem is that the nonlocal condition
contains the values of solution's derivatives at different points.
We prove the stability of this method in specific energy norm.
The main stability condition is that all eigenvalues of the corresponding
difference problem are positive. Results of computational experiments are presented.
Submitted October 9, 2021. Published June 30, 2022.
Math Subject Classifications: 65M06, 35K20, 34B10, 34K20.
Key Words: Nonlocal boundary conditions; parabolic equations;
alternating direction method; stability of finite difference scheme.
DOI: https://doi.org/10.58997/ejde.2022.44
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Mifodijus Sapagovas Institute of Data Science and Digital Technologies Vilnius University Akademijos str. 4, LT-04812, Vilnius, Lithuania email: mifodijus.sapagovas@mif.vu.lt |
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Jurij Novickij Institute of Data Science and Digital Technologies Vilnius University Akademijos str. 4, LT-04812 Vilnius, Lithuania email: jurij.novickij@mif.vu.lt |
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Regimantas Ciupaila Vilnius Gediminas Technical University Sauletekio ave. 11, LT-10223, Vilnius, Lithuania email: regimantas.ciupaila@vilniustech.lt |
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