Differential-algebraic equations index transformations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
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 '01 Proceedings of the International Conference on Computational Sciences-Part I
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In the paper we further develop the idea of parallel factorization of nonzero blocks of sparse coefficient matrices of the linear systems arising from discretization of large-scale index 1 differential-algebraic problems by Runge-Kutta methods and their following solving by Newton-type iterations. We formulate a number of theorems that give estimates for the local fill-in of such matrices on some stages of Gaussian elimination. As the result, we derive that only the suggested modification of Gauss method appeared to be effiective and economical one from the standpoint of CPU time and RAM.