Geodesic
On a Certain Finite-Difference Scheme for a Hereditary Oscillatory Equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 154 (2018), pp. 89-98

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In this paper, we proposed an explicit finite-difference scheme for numerical simulation of the Cauchy problem for a nonlinear integro-differential equation that describes an oscillatory process with friction and memory (heredity) and the corresponding local initial conditions. Approximation, stability, and convergence of the finite-difference scheme are examined. Results of computer experiments that implement the numerical scheme proposed confirm theoretical estimates.
Keywords: stability, explicit finite-difference scheme, heredity, integro-differential equation, memory function, Runge rule, approximation.
Mots-clés : convergence 
@article{INTO_2018_154_a10,
     author = {R. I. Parovik},
     title = {On a {Certain} {Finite-Difference} {Scheme} for a {Hereditary} {Oscillatory} {Equation}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {89--98},
     publisher = {mathdoc},
     volume = {154},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_154_a10/}
}
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R. I. Parovik. On a Certain Finite-Difference Scheme for a Hereditary Oscillatory Equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Tome 154 (2018), pp. 89-98. http://geodesic.mathdoc.fr/item/INTO_2018_154_a10/