M-matrices and convergence of finite difference scheme for parabolic equation with an integral boundary condition
Date
2020Author
Čiupaila, Regimantas
Sapagovas, Mifodijus
Pupalaigė, Kristina
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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.