Stabilized methods for the numerical solution of ODEs, also called Chebyshev methods, are explicit with extended stability domains along negative real axis. These intended large mildly stiff problems, originating mainly from parabolic PDEs. In this paper we present two-step Runge–Kutta–Chebyshev order two, which have more than 2.3 times larger intervals analogous one-step methods. Explicit form...

For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with built-in algorithm for finding the descent direction that forms an acute angle all subgradients in neighborhood current minimum. Minimizing function along opposite (with minus sign) enables to go beyond The algorithms is based on systems inequalities. finite convergen...