In scientific computing, it is time-consuming to calculate an inverse operator 𝓐 − 1 $\mathcal {A}^{-1}$ of a differential equation 𝓐 ϕ = f $\mathcal {A}\phi = f$ , especially when 𝓐 $\mathcal {A}$ is a highly nonlinear operator. In this paper, based on the homotopy analysis method (HAM), a new approach, namely the method of directly defining inverse… (More)