The use of extrapolation for the problem of computing accurate bifurcation values of periodic responses

The application of Richardson extrapolation to the problem of computing accurate bifurcation values of periodic responses is examined. It is shown that the numerical solutions computed by H. Kawakami's algorithm (see ibid., vol.CAS-31, no.3, p.248-260, 1984) have asymptotic error expansions if the trapezoidal rule is used for numerical integrations. Therefore, Richardson's extrapolation can be used to get high accuracy with relatively few computations. The effectiveness of this approach is also verified by a numerical example of Duffing's equation.<
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