Abstract The Radial Basis Function–Finite Difference Time Domain (RBF-FDTD) method was previously introduced by employing RBF approximations to replace conventional finite difference (FD) schemes for both spatial and temporal derivatives. In this work, we propose an alternative and simplified formulation of the RBF-FDTD technique, where RBF approximations are applied only to spatial derivatives, while temporal derivatives are discretized using conventional FD schemes. This approach is applied to simulate lightning-induced overvoltages on overhead power lines. An optimization algorithm for determining the shape parameter c x is also investigated to enhance numerical stability and accuracy. The performance of the developed method is evaluated against the conventional FDTD method using the LIOV solution as a benchmark. The numerical results demonstrate that the developed approach achieves better accuracy than the conventional FDTD method. Furthermore, the computational efficiency of the new approach is compared with that of the fully RBF-based FDTD method. These findings confirm that the proposed method is both accurate and computationally efficient, making it well-suited for practical electrical transient analyses.