GRE methods for nonlinear model of evolution equation and limited ressource environment

Michel, Philippe; Kakumani, Bhargav Kumar

doi:10.3934/dcdsb.2019161

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2022

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“…The existence, uniqueness, and the long time behavior of the solution for a particular type of non-linear MV-D were proved in [38]. The authors in [25,39] considered the nonlinear MV-D with Robin boundary data and proved the existence and uniqueness of its solution using the fixed point arguments. Moreover, the authors studied the asymptotic behavior of the solution towards its steady state using the notion of the General Relative Entropy.…”

Section: Introductionmentioning

confidence: 99%

A convergent numerical scheme to a parabolic equation with a nonlocal boundary condition

Kakumani¹,

Tumuluri²

2022

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In this paper, a numerical scheme for a nonlinear McKendrickvon Foerster equation with diffusion in age (MV-D) with the Dirichlet boundary condition is proposed. The main idea to derive the scheme is to use the discretization based on the method of characteristics to the convection part, and the finite difference method to the rest of the terms. The nonlocal terms are dealt with the quadrature methods. As a result, an implicit scheme is obtained for the boundary value problem under consideration. The consistency, and the convergence of the proposed numerical scheme is established. Moreover, numerical simulations are presented to validate the theoretical results.

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Section: Introductionmentioning

confidence: 99%