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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.

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
Full Text: DOI
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