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A four-stage index 2 diagonally implicit Runge-Kutta method. (English) Zbl 0993.65088
Summary: High index differential algebraic equations 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. Single diagonally implicit Runge-Kutta methods offer lower costs for integration. This paper derives a four-stage, index 2 explicit singly diagonally implicit Runge-Kutta 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.

##### MSC:
 65L80 Numerical methods for differential-algebraic equations 34A09 Implicit ordinary differential equations, differential-algebraic equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
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