A four-stage index 2 Diagonally Implicit Runge–Kutta method Original Research Article

High index Differential Algebraic Equations (DAEs) force standard numerical methods to lower order. Implicit Runge–Kutta methods such as RADAU5 handle high index problems but their fully implicit structure creates significant overhead costs for large problems. Singly Diagonally Implicit Runge–Kutta (SDIRK) methods offer lower costs for integration. This paper derives a four-stage, index 2 Explicit Singly Diagonally Implicit Runge–Kutta (ESDIRK) method. By introducing an explicit first stage, the method achieves second order stage calculations. After deriving and solving appropriate order conditions, numerical examples are used to test the proposed method using fixed and variable step size implementations.