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 
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/
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     title = {Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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