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On mathematical modeling of dermal and transdermal drug delivery.
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. Expand
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 forExpand
A general class of explicit pseudo two-step RKN methods on parallel computers
Abstract The aim of this paper is to investigate a general class of explicit pseudo two-step Runge-Kutta-Nystrom methods (RKN methods) of arbitrarily high order for nonstiff problems for systems ofExpand
Discretization based indices for semilinear partial differential algebraic equations
Abstract Semilinear partial differential algebraic equations (PDAEs) of the form Au t ( t , x ) + Bu xx ( t , x ) + F ( u ) = f ( t , x ) ( F ( u ) ∈ R n is a nonlinear function of u ∈ R n ), whereExpand
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 theseExpand
Partitioning strategies in Runge-Kutta type methods
The numerical solution of ode's suffers from stability constraints, if there are solution components with different time constants. Two recommended approaches in software packages to handle theseExpand
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.Expand
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 BetrachtungenExpand
Order results for Rosenbrock type methods on classes of stiff equations
SummaryIn this paper we give conditions for theB-convergence of Rosenbrock type methods when applied to stiff semi-linear systems. The convergence results are extended to stiff nonlinear systems inExpand