Difference Schemes with Nonuniform Meshes for Nonlinear Parabolic System (Journal of Computational Mathematics, 2021)
The boundary value problem for the nonlinear parabolic system is solved by the finite difference method with nonuniform meshes. The existence and a priori estimates of the discrete vector solutions for the general difference schemes with unequal meshsteps are established by the fixed point technique. The absolute and relative convergence of the discrete vector solution are justified by a series of a priori estimates. The analysis of mentioned problems is based on the assumption of heuristic character concerning the existence of the unique smooth solution for the original problem of the nonlinear parabolic system.