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Diagonally implicit Runge-Kutta methods for differential algebraic equations of indices two and three. (Russian, English) Zbl 1224.65176
Zh. Vychisl. Mat. Mat. Fiz. 50, No. 6, 1047-1059 (2010); translation in Comput. Math., Math. Phys. 50, No. 6, 993-1005(2010).
Summary: Diagonally implicit Runge-Kutta methods satisfying additional order conditions are examined. These conditions make it possible to solve differential algebraic equations of indices two and three to higher accuracy. Advantages of the proposed methods over other known techniques are demonstrated using test problems.

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L80 Numerical methods for differential-algebraic equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
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