Numerical solution to a nonlinear McKendrick-Von Foerster equation with diffusion

Numerical solution to a nonlinear McKendrick-Von Foerster equation with diffusion

An implicit finite difference scheme is presented to approximate the solution to the McKendrick-Von Foerster equation with diffusion (M-V-D). The notion of upper solution is introduced and used effectively with aid of discrete maximum principle to study the well-posedness and stability of the numeri...

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Veröffentlicht in:Numerical algorithms 2023-02, Vol.92 (2), p.1007-1039
Hauptverfasser: Halder, Joydev, Tumuluri, Suman Kumar
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algorithms
Approximation
Boundary conditions
Computer Science
Finite difference method
Maximum principle
Numeric Computing
Numerical Analysis
Original Paper
Partial differential equations
Theory of Computation
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Zusammenfassung:An implicit finite difference scheme is presented to approximate the solution to the McKendrick-Von Foerster equation with diffusion (M-V-D). The notion of upper solution is introduced and used effectively with aid of discrete maximum principle to study the well-posedness and stability of the numerical scheme. A relation between the numerical solutions to the M-V-D and the steady state problem is established.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01328-5