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<p>An approach to the determination of the convergence control parameter (coefficient) in the homotopy analysis method with the use of the boundary relations constructed on the basis of the double integration of the nonlinear differential equation is proposed. As an example, the approximate solution of the problem on the cooling of a thin rib with radiation heat transfer and the problem on the flow of the third-power non-Newtonian fluid on a moving band was considered. An indubitable advantage of the approach proposed over the classical computational algorithm, according to which the squared residual of the differential equation is minimized, was revealed.</p>

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Boundary Integral Relations as an Efficient Instrument of Finding the Control Parameter in the Homotopy Analysis Method

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • V. A. Kot

摘要

An approach to the determination of the convergence control parameter (coefficient) in the homotopy analysis method with the use of the boundary relations constructed on the basis of the double integration of the nonlinear differential equation is proposed. As an example, the approximate solution of the problem on the cooling of a thin rib with radiation heat transfer and the problem on the flow of the third-power non-Newtonian fluid on a moving band was considered. An indubitable advantage of the approach proposed over the classical computational algorithm, according to which the squared residual of the differential equation is minimized, was revealed.