Geodesic
Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 119-142
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New approach to constructing methods of Runge–Kutta type as well as multistep methods for solving functional-differential equations is proposed. Our methods (direct analogs of numerical methods for solving ordinary differential equations) are based on separation of finite-dimensional and infinite-dimensional (functional) components in the structure of the phase state. Determination of the approximation order of the methods essentially uses notions of $i$-smooth analysis. 
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     author = {A. V. Kim and V. G. Pimenov},
     title = {Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {119--142},
     year = {1998},
     volume = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a10/}
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A. V. Kim; V. G. Pimenov. Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 119-142. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a10/