Geodesic
Decomposition method of solving connected systems of differential equations of hyperbolic type
Matematičeskoe modelirovanie, Tome 3 (1991) no. 9, pp. 76-86.

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A numerical method for solving connected systems of differential equations is proposed. The method is aimed for the calculation of unsteady non-isotermic states of gas transport along a pipeline system of arbitrary configuration. The proposed iterative method is based on a decomposition approach. The solving of the main problem at each time step is provided by two stages. At first stage the main problem is divided into the subproblems of more simple structure and lower dimension. At the second stage the subproblems are co-ordinated. The solving process is being continued till the parameters of gas flow in the pipeline nodes are consisted with the parameters in the lines. The parallel computations are possible. 
@article{MM_1991_3_9_a6,
     author = {A. D. Teviashev and I. G. Gusarova},
     title = {Decomposition method of solving connected systems of differential equations of hyperbolic type},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {76--86},
     publisher = {mathdoc},
     volume = {3},
     number = {9},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1991_3_9_a6/}
}
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A. D. Teviashev; I. G. Gusarova. Decomposition method of solving connected systems of differential equations of hyperbolic type. Matematičeskoe modelirovanie, Tome 3 (1991) no. 9, pp. 76-86. http://geodesic.mathdoc.fr/item/MM_1991_3_9_a6/