Finite Volume Approximations for Size Structured Neuron Model
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The objective of this paper is to present and analyze numerical approximation for the size structured neuron model. We propose finite volume approximations based on upwind and Lax–Wendroff for the partial differential equation originating in size structured neuron model (Perthame and Ryzhik in J Differ Equ 210:155–177, 2005) which is a conservation laws with source term. The developed numerical methods are analyzed for consistency, stability, and convergence. We perform some numerical experiments to verify the predicted theory of the numerical approximations constructed in this paper.
KeywordsHyperbolic conservation laws Finite volume approximation Size structured neuron model
Mathematics Subject Classification35L04 35L65 65M08 92B20
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Conflicts of interest
The authors declare that they have no conflict of interest.
The author Mr. Santosh Kumar is thankful to the University Grants Commission, Government of India for providing financial assistance in terms of Junior Research Fellowship (F. 2-16/2011(SA-I)). The authors are thankful to the anonymous referees for their invaluable suggestions.
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