Geodesic
On Decomposition of Difference Schemes for Numerical Solution of Differential Algebraic Equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 88-100

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We consider quasi-linear systems of ordinary differential equations (ODE) with identically singular matrix multiplying the derivative of the desired vector-function and difference scheme for their numerical solution. We discuss conditions that make it possible to solve algebraic (finite-dimensional) equations at each step of numerical process and substitute the solutions obtained into the dynamics equations. Results of numerical solution of ODE systems modeling direct-flow boiler unit are given.
Keywords: differential-algebraic equations, index, difference schemes, mathematical models, direct-flow boiler. 
@article{VYURU_2012_11_a8,
     author = {V. F. Chistyakov and E. A. Tairov and E. V. Chistyakova and A. A. Levin},
     title = {On {Decomposition} of  {Difference} {Schemes} for {Numerical} {Solution} of  {Differential} {Algebraic} {Equations}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {88--100},
     publisher = {mathdoc},
     number = {11},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2012_11_a8/}
}
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V. F. Chistyakov; E. A. Tairov; E. V. Chistyakova; A. A. Levin. On Decomposition of  Difference Schemes for Numerical Solution of  Differential Algebraic Equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, no. 11 (2012), pp. 88-100. http://geodesic.mathdoc.fr/item/VYURU_2012_11_a8/