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On mathematical modeling of dermal and transdermal drug delivery.
TLDR
A model is developed that can predict both the concentration profile and the position of the penetration boundary depending on time and is described on a two-dimensional multilayered domain representing a cross section through human skin.
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B-convergence results for linearly implicit one step methods
B-consistency andB-convergence of linearly implicit one step methods with respect to a class of arbitrarily stiff semi-linear problems are considered. Order conditions are derived. An algorithm for…
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A general class of explicit pseudo two-step RKN methods on parallel computers
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Discretization based indices for semilinear partial differential algebraic equations
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Indexes and Special Discretization Methods for Linear partial Differential Algebraic Equations
Linear partial differential algebraic equations (PDAEs) of the form Aut(t, x) + Buxx(t, x) + Cu(t, x) = f(t, x) are studied where at least one of the matrices A, B ∈ Rn×n is singular. For these…
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Partitioning strategies in Runge-Kutta type methods
TLDR
The numerical solution of ode's suffers from stability constraints, if there are solution components with different time constants, and the use of partitioned methods for a given splitting into stiff and nonstiff subsystems is investigated.
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On error behaviour of partitioned linearly implicit runge-kutta methods for stiff and differential algebraic systems
This paper studies partitioned linearly implicit Runge-Kutta methods as applied to approximate the smooth solution of a perturbed problem with stepsizes larger than the stiffness parameterε.…
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Hairer, E.; Norsett, S. P.; Wanner, G., Solving Ordinary Differential Equations. I: Nonstiff Problems. Berlin etc., Springer-Verlag 1987. XIV, 480 pp., 105 figs., DM 124,—. ISBN 3-540-17145-2…
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Linear-implizite Runge-Kutta-Methoden
In diesem Kapitel untersuchen wir linear-implizite RK-Methoden. Es werden die bewahrten Klassen der adaptiven RK-Methoden und der Rosenbrock-Typ-Methoden vorgestellt. Im Mittelpunkt der Betrachtungen…
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On the numerical integration of second-order initial value problems with a periodic forcing function
TLDR
For a family of second-order explicit and linearly implicit Runge-Kutta-Nyström methods it is shown that the forced oscillation is represented with zero phase lag.
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