Numerical realization of the method of functional-analytic series for projecting on a stable manifold

The problem of initial data projecting on a stable manifold for a Chafee-Infante-type equation is solved numerically by the method of functional-analytic series. Several computational formulas are deduced, some peculiarities of practical realization are discussed, and a number of numerical results obtained for the case of quadratic nonlinearity are presented.