• Corpus ID: 246275881

A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition

@article{Halder2022ANS,
  title={A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition},
  author={Joydev Halder and Suman Kumar Tumuluri},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.10440}
}
In this article, a numerical scheme to find approximate solutions to the McKendrick-Von Foerster equation with diffusion (M-V-D) is presented. The main difficulty in employing the standard analysis to study the properties of this scheme is due to presence of nonlinear and nonlocal term in the Robin boundary condition in the M-V-D. To overcome this, we use the abstract theory of discretizations based on the notion of stability threshold to analyze the scheme. Stability, and convergence of the… 

References

SHOWING 1-10 OF 27 REFERENCES
Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions
In this paper, we consider a particular type of nonlinear McKend-rick-von Foerster equation with a diffusion term and Robin boundary condition. We prove the existence of a global solution to this
A numerical scheme to the McKendrick–von Foerster equation with diffusion in age
In this paper a numerical scheme for McKendrick–von Foerster equation with diffusion in age (MV‐D) is proposed. First, we discretize the time variable to get a second‐order ordinary differential
Asymptotic behavior for a class of the renewal nonlinear equation with diffusion
In this paper, we consider nonlinear age‐structured equation with diffusion under nonlocal boundary condition and non‐negative initial data. More precisely, we prove that under some assumptions on
On a nonlinear renewal equation with diffusion
In this paper, we consider a nonlinear age structured McKendrick–von Foerster population model with diffusion term. Here we prove existence and uniqueness of the solution of the equation. We consider
Heat Conduction Within Linear Thermoelasticity
1 Preliminaries.- 1.1 One-dimensional linear thermoelasticity.- 1.2 An energy integral.- 2 The Coupled and Quasi-static Approximation.- 2.1 An integro-differential equation.- 2.2 Construction of
Analysis of Discretization Methods for Ordinary Differential Equations
TLDR
The Discretization Methodology helps clarify the meaning of Consistency, Convergence, and Stability with Forward Step Methods and provides a guide to applications of Asymptotic Expansions in Even Powers of n.
Extensions of a property of the heat equation to linear thermoelasticity and other theories
is a decreasing function of t for 0 < t < T. It should be noted that (P) holds whatever initial values the temperature may take on f = 0. The adjective 'decreasing' is to be understood in the wide
Mathematical biology
TLDR
The aim of this study was to investigate the bifurcations and attractors of the nonlinear dynamics model of the saccadic system, in order to obtain a classification of the simulated oculomotor behaviours.
A note on a neuron network model with diffusion
We study the dynamics of an inhomogeneous neuronal network parametrized by a real number \begin{document}$ \sigma $\end{document} and structured by the time elapsed since the last discharge. The
...
...