A new homotopy-based approach is proposed, embodied in the Limit Homotopy Decomposition Method (LHDM). This method departs from a fundamental property of standard homotopy constructions – namely, the requirement that the original nonlinear differential equation be fully preserved at the parameter value p = 1. In the proposed approach, the original form of the nonlinear differential equation is modified at p = 1 by introducing a coefficient (a matching parameter) multiplying the nonlinear term; this coefficient approaches unity as the order of approximation increases (M → ∞). This approach enables the derivation of approximate analytical solutions for boundary-value problems governed by nonlinear differential equations in a simpler form. Using LHDM, an approximate solution was obtained for the problem of radiative heat transfer in a thin rectangular fin. It is demonstrated that LHDM yields analytical solutions that are more compact and simpler in form than those obtained via the standard version of the Optimal Homotopy Analysis Method (OHAM), while maintaining comparable accuracy. Furthermore, the matching parameter rapidly C M/N approaches its limiting value of unity with each successive approximation. These results suggest that the proposed LHDM is a viable alternative to the standard OHAM.

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