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Implicit Runge-Kutta methods for transferable differential-algebraic equations

M. Arnold (1994)

Banach Center Publications

The numerical solution of transferable differential-algebraic equations (DAE’s) by implicit Runge-Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is non-singular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE’s with smooth solution we get convergence of order m i n ( k E , k I + 1 ) , where k E is the classical order of the IRK and k I is the stage order. For transferable...

Input-output systems in Biology and Chemistry and a class of mathematical models describing them

Erich Bohl, Ivo Marek (2005)

Applications of Mathematics

Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators...

Integral Equivalence of Two Systems of Differential Equations

Jarosław Morchało (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studia l'equivalenza asintotica fra le soluzioni di un sistema lineare e quelle di una perturbazione non lineare. Vengono date condizioni sufficienti per l'esistenza di un omeomorfìsmo fra le soluzioni limitate di tali sistemi.

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