Differential-algebraic equations index transformations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
Convergence theorems for iterative Runge-Kutta methods with a constant integration step
Computational Mathematics and Mathematical Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
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In the paper we study how to integrate numerically large-scale systems of semi-explicit index 1 differential-algebraic equations by implicit Runge-Kutta methods. In this case, if Newton-type iterations are applied to the discrete problems we need to solve high dimension linear systems with sparse coefficient matrices. Therefore we develop an effective way for packing such matrices of coefficients and derive special Gaussian elimination for parallel factorization of nonzero blocks of the matrices. As a result, we produce a new efficient procedure to solve linear systems arising from application of Newton iterations to the discretizations of large-scale index 1 differential-algebraic equations obtained by implicit Runge-Kutta methods. Numerical tests support theoretical results of the paper.