Reducibility and characterization of symplectic Runge-Kutta methods.
Regularity and approximability of the solutions to the chemical master equation
The chemical master equation is a fundamental equation in chemical kinetics. It underlies the classical reaction-rate equations and takes stochastic effects into account. In this paper we give a simple argument showing that the solutions of a large class of chemical master equations are bounded in weighted ℓ1-spaces and possess high-order moments. This class includes all equations in which no reactions between two or more already present molecules and further external reactants occur that add mass...
Regularization of nonlinear ill-posed problems by exponential integrators
The numerical solution of ill-posed problems requires suitable regularization techniques. One possible option is to consider time integration methods to solve the Showalter differential equation numerically. The stopping time of the numerical integrator corresponds to the regularization parameter. A number of well-known regularization methods such as the Landweber iteration or the Levenberg-Marquardt method can be interpreted as variants of the Euler method for solving the Showalter differential...
Resolution of first- and second-order linear differential equations with periodic inputs by a computer algebra system.
Richardson Extrapolation combined with the sequential splitting procedure and the θ-method
Initial value problems for systems of ordinary differential equations (ODEs) are solved numerically by using a combination of (a) the θ-method, (b) the sequential splitting procedure and (c) Richardson Extrapolation. Stability results for the combined numerical method are proved. It is shown, by using numerical experiments, that if the combined numerical method is stable, then it behaves as a second-order method.
Rosenbrock Methods for Differential Algebraic Equations.
Round-off Error for Retarded Ordinary Differential Equations: A Priori Bounds and Estimates.
Runge-Kutta-Verfahren mit festen und variablen Parametern zur Lösung von Systemen gewöhnlicher Differentialgleichungen 1. Ordnung