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Stable solutions to homogeneous difference-differential equations with constant coefficients: Analytical instruments and an application to monetary theory

Ulf von Kalckreuth, Manfred Krtscha (2004)

Applications of Mathematics

In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schröder. Working out its stability properties, we...

The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations

Sulkhan Mukhigulashvili (2013)

Czechoslovak Mathematical Journal

The a priori boundedness principle is proved for the Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Several sufficient conditions of solvability of the Dirichlet problem under consideration are derived from the a priori boundedness principle. The proof of the a priori boundedness principle is based on the Agarwal-Kiguradze type theorems, which guarantee the existence of the Fredholm property for strongly singular higher-order linear...

The norm convergence of a Magnus expansion method

András Bátkai, Eszter Sikolya (2012)

Open Mathematics

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method is investigated.

The periodic problem for the second order integro-differential equations with distributed deviation

Sulkhan Mukhigulashvili, Veronika Novotná (2021)

Mathematica Bohemica

We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation u ' ' ( t ) = p 0 ( t ) u ( t ) + ∫ 0 ω p ( t , s ) u ( τ ( t , s ) ) d s + q ( t ) , and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.

Time delay in chemical exchange during an NMR pulse

Dan Gamliel (2014)

Mathematica Bohemica

Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all...

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