Multilevel explicit schemes and their stability (Q2730691)

The authors propose a new approach to the construction of explicit schemes for solving initial boundary value problems for parabolic equations. Multilevel explicit schemes based on the conjugation conditions corresponding to the Neumann problem and localizing the stability conditions are constructed. For composite explicit schemes in abstract form sufficient stability conditions with respect to the initial data and to the right-hand side are proved. Results on the two-dimensional heat conduction equation in a bounded polygon with approximation in the framework of the domain decomposition method and the finite element method are illustrated.