On the solution of characteristic value problems arising in linear stability analysis; semi analytical approach

Abstract The linear stability analysis is normally governed by equations that constitute an eigenvalue (characteristic value) problem. In this paper, for the first time, two semi analytical algorithms, (1) Differential Transform Method (DTM) and (2) Adomian Decomposition Method (ADM) are examined for solving a characteristic value problem occurring in linear stability analysis. In this paper, the characteristic value problem of Couette Taylor flow is selected because its simple geometry continues to be a paradigm for theoretical studies of hydrodynamic stability. The results show that DTM handles the solution conveniently and accurately. However, this paper limits the use of ADM for solving characteristic value problems. The results indicate that the present algorithm based on DTM could be used as a promising method for solving characteristic value problems.

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