Geodesic
Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1594-1608

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A boundary value problem is examined for a linear differential algebraic system of partial differential equations with a special structure of the associate matrix pencil. The use of an appropriate transformation makes it possible to split such a system into a system of ordinary differential equations, a hyperbolic system, and a linear algebraic system. A three-layer finite difference method is applied to solve the resulting problem numerically. A theorem on the stability and the convergence of this method is proved, and some numerical results are presented. 
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     author = {S. V. Gaidomak},
     title = {Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1594--1608},
     publisher = {mathdoc},
     volume = {49},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a6/}
}
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S. V. Gaidomak. Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1594-1608. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a6/