Geodesic
Numerical solving of partial differential equations with heredity and nonlinearity in the differential operator
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1587-1599

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The problem to be considered is a numerical solving of nonlinear partial differential equations with heredity effect. Nonlinearity is contained in the operator of differentiation as well as in the inhomogeneity function. We propose a nonlinear implicit difference scheme, which implies the use of iterative methods to find the solution on each time layer. To take into account the heredity effect the interpolation and extrapolation of grid solution were used. Stability and convergence of the proposed difference scheme were proved. Numerical experiments were carried out and results coincides with the theoretical ones.
Keywords: nonlinear difference scheme, convergence of the difference scheme, partial differential equation, time delay. 
@article{SEMR_2019_16_a118,
     author = {T. V. Gorbova and V. G. Pimenov and S. I. Solodushkin},
     title = {Numerical solving of partial differential equations with heredity and nonlinearity in the differential operator},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1587--1599},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a118/}
}
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T. V. Gorbova; V. G. Pimenov; S. I. Solodushkin. Numerical solving of partial differential equations with heredity and nonlinearity in the differential operator. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1587-1599. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a118/