M-matrices and convergence of finite difference scheme for parabolic equation with integral boundary condition

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.

Keywords

• finite difference method
• nonlocal boundary condition
• convergence
• M-matrices