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Diagonally implicit Runge—Kutta methods for differential algebraic equations of indices two and three

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Abstract

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.

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Authors and Affiliations

  1. Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

    L. M. Skvortsov

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  1. L. M. Skvortsov
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Correspondence to L. M. Skvortsov.

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Original Russian Text © L.M. Skvortsov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 6, pp. 1047–1059.

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Skvortsov, L.M. Diagonally implicit Runge—Kutta methods for differential algebraic equations of indices two and three. Comput. Math. and Math. Phys. 50, 993–1005 (2010). https://doi.org/10.1134/S0965542510060072

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