Asymptotic analysis to Von Kármán swirling-flow problem

In this paper, we consider the Von Kármán swirling-flow problem, which is described by an ordinary equations system. The explicit asymptotic solutions are given by applying the homotopy renormalization method. Furthermore, the numerical simulations verify that our asymptotic solutions have high precision and the absolute errors are less than 0.03, which means that the results obtained are truly valid and can be used practically.

Asymptotic analysis to free-convective boundary-layer problem by homotopy renormalization method

In this paper, the homotopy renormalization (HTR) method is applied to investigate a free-convective boundary-layer problem arising from the sheet (or fiber) manufacturing, which is modeled by a system of nonlinear ordinary differential equations. By taking the inhomogeneous variable coefficient homotopy equations, the explicit asymptotic solutions satisfying the boundary conditions are given. Moreover, the comparisons with the numerical results show that our explicit function solutions have good performances in both local and large scales.

Asymptotic Analysis of a Nonlinear Problem on Domain Boundaries in Convection Patterns by Homotopy Renormalization Method

In this article, using the homotopy renormalization method, the asymptotic analysis to a nonlinear problem on domain boundaries in convection patterns are given. In particular, by taking a variable coefficient homotopy equation, the global asymptotic solutions satisfying boundary conditions are obtained. These results are better than the existing analytic approximation solutions.