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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 10 > No. 1


Discrete Analogs of the Comparison Theorem and Two-Sided Estimates of Solution of Parabolic Equations

PP: 83-92
Piotr Matus, Ryszard Kozera, Agnieszka Paradzinska, Denis Schadinskii,
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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