Geodesic
On application of the $i$-smooth analysis methodology to~elaboration of numerical methods for solving functional~differential~equations
Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 133, pp. 26-34

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The article discusses a number of aspects of the application of $i$-smooth analysis in the development of numerical methods for solving functional differential equations (FDE). The principle of separating finite- and infinite-dimensional components in the structure of numerical schemes for FDE is demonstrated with concrete examples, as well as the usage of different types of prehistory interpolation, those by Lagrange and Hermite. A general approach to constructing Runge–Kutta-like numerical methods for nonlinear neutral differential equations is presented. Convergence conditions are obtained and the order of convergence of such methods is established.
Keywords: functional differential equations; numerical methods; $i$-smooth analysis; systems with delays. 
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     author = {A. V. Kim},
     title = {On application of the $i$-smooth analysis methodology to~elaboration of numerical methods for solving functional~differential~equations},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {26--34},
     publisher = {mathdoc},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/VTAMU_2021_26_133_a2/}
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A. V. Kim. On application of the $i$-smooth analysis methodology to~elaboration of numerical methods for solving functional~differential~equations. Vestnik rossijskih universitetov. Matematika, Tome 26 (2021) no. 133, pp. 26-34. http://geodesic.mathdoc.fr/item/VTAMU_2021_26_133_a2/