The efficiency of the analytical method of extension of boundaries is shown using phase transformations as an example. The initial problem is replaced by an auxiliary one where rectangular regions with known eigenfunctions and eigenvalues are made to correspond to curvilinear regions with moving boundaries of each phase. This enables us to represent the solution by expansions in improved Fourier series differing from the classical ones by an increased convergence rate. Finally, the problem is reduced to a small number of differential equations of first order in time.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 3, pp. 576–585, May–June, 2009.
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Chernyshov, A.D. Solution of phase-transformation problems by the method of extension of boundaries. J Eng Phys Thermophy 82, 574–583 (2009). https://doi.org/10.1007/s10891-009-0218-5
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DOI: https://doi.org/10.1007/s10891-009-0218-5