Stability conditions for method of self-similar approximations

Abstract

A generalization for the method of self‐similar approximations suggested recently by the author is given. Stability conditions for the method are formulated: first, the mapping multipliers for the self‐similar recurrence relations have to be less than unity; second, the Lyapunov exponent for the differential form of the self‐similar relations has to be negative. The fixed‐point conditions defining the governing functions are analyzed from the point of view of stability. It is shown that the fixed‐point condition expressed in the form of the principle of minimal sensitivity provides a contracting mapping contrary to the condition in the form of the principle of minimal difference. This explains why, in general, the former fixed‐point condition yields more accurate results than the latter.