A new block method with variable stepsize implementation for solving third‐order differential systems

This article presents an efficient one‐step hybrid block method (OHBM) to solve third‐order initial value problems (IVPs). The proposed method is derived using interpolation and collocation techniques of the assumed exact solution and its derivatives. The theoretical properties of the OHBM are analyzed. An embedding‐like technique is utilized and executed in an adaptive mode to improve the performance of the proposed method. The OHBM's efficiency and accuracy are tested by solving practical application problems in applied sciences and engineering. The numerical solutions demonstrate that the proposed OHBM is highly efficient and provides very accurate approximations.