Geodesic
The Rothe method for the McKendrick-von Foerster equation
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 3, pp. 589-602
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We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in $L^\infty $ and $L^1$ norms. Proofs of these results are based on comparison inequalities. Our theory is illustrated by numerical experiments. Our research is motivated by certain models of mathematical biology.
We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in $L^\infty $ and $L^1$ norms. Proofs of these results are based on comparison inequalities. Our theory is illustrated by numerical experiments. Our research is motivated by certain models of mathematical biology.
DOI : 10.1007/s10587-013-0042-0
Classification : 65M12, 65M99, 92B99
Keywords: Rothe method; stability; comparison 
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Leszczyński, Henryk; Zwierkowski, Piotr. The Rothe method for the McKendrick-von Foerster equation. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 3, pp. 589-602. doi: 10.1007/s10587-013-0042-0

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