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<p>A review and a critical analysis of modern advanced semi-analytical methods, such as the perturbation method, the homotopy perturbation method, the variational iteration method, the homotopy analysis method, the Taylor series method, the successive differentiation method, the differential transformation method, the Adomian decomposition method, and the optimal homotopy asymptotic method, are presented. These methods were investigated by the example of approximate solving a nonlinear initial-value problem on the convective cooling of a system with lumped parameters and a temperature-dependent heat capacity.</p>

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Nonlinear Problem on Convective Heat Exchange: Advanced Semi-Analytical Solution Methods (Review and Critical Analysis)

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • V. A. Kot

摘要

A review and a critical analysis of modern advanced semi-analytical methods, such as the perturbation method, the homotopy perturbation method, the variational iteration method, the homotopy analysis method, the Taylor series method, the successive differentiation method, the differential transformation method, the Adomian decomposition method, and the optimal homotopy asymptotic method, are presented. These methods were investigated by the example of approximate solving a nonlinear initial-value problem on the convective cooling of a system with lumped parameters and a temperature-dependent heat capacity.