β Scribed by A.A. Samarskii; P.P. Matus; V.I. Mazhukin; I.E. Mozolevski
No coin nor oath required. For personal study only.
There are considered elliptic and parabolic equations of arbitrary dimension with alternating coefficients at mixed derivatives. For such equations, monotone difference schemes of the second order of local approximation are constructed. Schemes suggested satisfy the principle of maximum. A priori estimates of stability in the norm C without limitation on the grid steps T and h,, a = 1,2 ,..., p are obtained (unconditional stability).
π SIMILAR VOLUMES
Monotone finite difference schemes are proposed for nonlinear systems with mixed quasi-monotonicity. Two monotone iteration processes for the corresponding discrete problems are presented, which converge monotonically to the quasisolutions of the discrete problems. The limits are the exact solutions
## Abstract The discrete mollification method is a convolutionβbased filtering procedure suitable for the regularization of illβposed problems and for the stabilization of explicit schemes for the solution of PDEs. This method is applied to the discretization of the diffusive terms of a known first