We study the behavior of Lagrangian perturbative solutions. For a spherical void model, the higherorder the Lagrangian perturbation we consider, the worse the approximation becomes in late-timeevolution. In particular, if we stop to improve until an even order is reached, the perturbative solutiondescribes the contraction of the void. To solve this problem, we consider improving the perturbativesolution using Shanks transformation, which accelerates the convergence of the sequence. After thetransformation, we find that the accuracy of higher-order perturbation is recovered and the perturbativesolution is refined well. Then we show that this improvement method can apply for a CDM model andimproved the power spectrum of the density field.
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