Geodesic
Implicit difference methods for evolution functional differential equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 361-379.

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A general theory of implicit difference schemes for nonlinear functional differential equations with initial boundary conditions is presented. A theorem on error estimates of approximate solutions for implicit functional difference equations of the Volterra type with an unknown function of several variables is given. This general result is employed to investigate the stability of implicit difference schemes generated by first-order partial differential functional equations and by parabolic problems. A comparison technique with nonlinear estimates of the Perron type for given functions with respect to the functional variable is used. 
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Z. Kamont; K. Kropielnicka. Implicit difference methods for evolution functional differential equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 361-379. http://geodesic.mathdoc.fr/item/SJVM_2011_14_4_a2/

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