M-MATRICES AND CONVERGENCE OF FINITE DIFFERENCE SCHEME FOR PARABOLIC EQUATION WITH INTEGRAL BOUNDARY CONDITION-Reference-Cited by-同舟云学术

M-MATRICES AND CONVERGENCE OF FINITE DIFFERENCE SCHEME FOR PARABOLIC EQUATION WITH INTEGRAL BOUNDARY CONDITION

Published:2020-03-18 Issue:2 Volume:25 Page:167-183
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Čiupaila Regimantas¹,Sapagovas Mifodijus²,Pupalaigė Kristina³

Affiliation:

1. Vilnius Gediminas Technical University, Saulėtekio av. 11, LT-10223, Vilnius, Lithuania

2. Faculty of Mathematics and Informatics, Vilnius University, Akademijos str. 4, LT-08412, Vilnius, Lithuania

3. Department of Applied Mathematics, Kaunas University of Technology, Studentų str. 50, LT-51368, Kaunas, Lithuania

Abstract

In the paper, the stability and convergence of difference schemes approximating semilinear parabolic equation with a nonlocal condition are considered. The proof is based on the properties of M-matrices, not requiring the symmetry or diagonal predominance of difference problem. The main presumption is that all the eigenvalues of the corresponding difference problem with nonlocal conditions are positive.

Publisher

Vilnius Gediminas Technical University

Subject

Modelling and Simulation,Analysis

Reference38 articles.

1. Nonnegative Matrices in the Mathematical Sciences

2. Stepwise Stability for the Heat Equation with a Nonlocal Constraint

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5. A parabolic equation with nonlocal boundary conditions arising from electrochemistry

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