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The linear master equation (ME) describing the stochastic kinetics ofIsing-type models has been transformed into a nonlinear ME (NLME) for atime-dependent effective Hamiltonian (EH). It has been argued that for modelswith large number of spins ($N$) NLME is easier to deal with numerically thanME. The reason is that the non-equilibrium probability distribution entering MEscales exponentially with the system size which for large $N$ causes numericalunder- and overflow problems. NLME, in contrast, contains quantities scalingwith $ N $ not faster than linearly.  The advantages of NLME in numerical calculations has been illustrated on theproblem of decay of metastable states in the kinetic Husimi-Temperley model(HTM) previously studied within ME approach by other authors. It has been shownthat the use of NLME makes possible to extend by orders of magnitude the rangesof numerically accessible quantities, such as the system size $ N $ and thelifetimes of metastable states, as well as the accuracy of the calculations. Anexcellent agreement of numerical results with previous studies has been found.  It has been shown that in the thermodynamic limit EH for HTM exactlysatisfies a nonlinear first order differential equation. The system ofcharacteristic equations for its solution has been derived and it has beenshown that the conventional mean field equation is one of them.

Effective Hamiltonian approach to the kinetic infinitely long-range Ising (the Husimi-Temperley) model