abstract:In this paper, a new time-like function with the incorporation of the fictitious time integration method (FTIM) is proposed. The new time-like function is modified from the original time-like function in the FTIM by adding a control parameter m, which dramatically improves the performance of the FTIM for solving highly nonlinear boundary value problems (BVPs) and plays as an important controller to assure the convergence of the solution during the time integration process. The requirements and the characteristics of the new time-like function are presented by examining the FTIM through the perspective of the new time-like function in which the limitation and the possible paths of improvement can be clarified. Several applications, including two- dimensional and three-dimensional BVPs using the FTIM with the new time-like function, are conducted. Results obtained demonstrate that the FTIM with the proposed time-like function can significantly improve accuracy as well as convergence. With the advantages and ease of numerical implementation, the new time-like function proposed in this study is seen to be a better alternative for the FTIM.