Absolutely stable numerical algorithm for hyperbolic equations of the first order (Q2703314)

The author proposes a generalization of the two-step finite difference method of second order accuracy for a solution of the system \({\partial u\over \partial t}+\sum_{i=1}^{3} {\partial F^{i}(u)\over\partial x_{i}}=0\), \((x,t)\in G= \{(x_1,x_2,x_3,t):0\leq x_{i}\leq 1\), \(i=1,2,3\), \(t>t_0\}\), with given initial and boundary value conditions. Stability of the proposed algorithm is proved. Properties of dispersibility and dissipativity are studied.