M-matrices and convergence of finite difference scheme for parabolic equation with integral boundary condition - Čiupaila, Regimantas; Sapagovas, Mifodijus; Pupalaigė, Kristina (Mathematical Modelling and Analysis, 2020)
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.