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A numerical scheme to the McKendrick–von Foerster equation with diffusion in age
Author(s) -
Kakumani Bhargav Kumar,
Tumuluri Suman Kumar
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22280
Subject(s) - mathematics , ode , discretization , ordinary differential equation , convergence (economics) , piecewise , scheme (mathematics) , stability (learning theory) , piecewise linear function , variable (mathematics) , partial differential equation , mathematical analysis , numerical analysis , differential equation , computer science , machine learning , economics , economic growth
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 equation (ODE). At each time level, well‐posedness of this ODE is established using classical methods. Stability estimates for this semidiscrete scheme are derived. Later we construct piecewise linear (in time) functions using the solutions of the semidiscrete problems to approximate the solution to MV‐D and establish the convergence result. Numerical results are presented in some cases and compared with the corresponding analytic solutions where the latter is known explicitly.