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Discrete Analogs of the Comparison Theorem and Two-Sided Estimates of Solution of Parabolic Equations |
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PP: 83-92 |
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doi:10.18576/amis/100108
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Author(s) |
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Piotr Matus,
Ryszard Kozera,
Agnieszka Paradzinska,
Denis Schadinskii,
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Abstract |
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| In this paper, we prove the difference analogs of the comparison theorems for solutions of the Cauchy problem for a
nonlinear ordinary differential equation (ODE). These theorems are used to analyse blow-up solution of finite-difference schemes
(FDS) approximating the Neumann problem for a parabolic equation with a nonlinear source of power form. We also propose the
method for obtaining the two-sided estimates of solution. This method is based on implicit and explicit FDS. |
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