Geodesic
On the stability of an implicit spline collocation difference scheme for linear partial differential algebraic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 9, pp. 1460-1479

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A boundary value problem for linear partial differential algebraic systems of equations with multiple characteristic curves is examined. It is assumed that the pencil of matrix functions associated with this system is smoothly equivalent to a special canonic form. The spline collocation is used to construct for this problem a difference scheme of an arbitrary approximation order with respect to each independent variable. Sufficient conditions are found for this scheme to be absolutely stable. 
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     author = {S. V. Gaidomak},
     title = {On the stability of an implicit spline collocation difference scheme for linear partial differential algebraic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1460--1479},
     publisher = {mathdoc},
     volume = {53},
     number = {9},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_9_a3/}
}
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S. V. Gaidomak. On the stability of an implicit spline collocation difference scheme for linear partial differential algebraic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 9, pp. 1460-1479. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_9_a3/