The paper introduces new classes of numerical ODE solvers that base their internal discretization method on state quantization instead of time slicing. These solvers have been coined Quantized State System (QSS) simulators. The main result of this work is a first order accurate QSS-based stiff system solver called Backward QSS (BQSS). The numerical properties of this new algorithm are being dis...

In this paper, we prove the local controllability to positive constant trajectories of a nonlinear system two coupled ODE equations, posed in one-dimensional spatial setting, with nonlocal nonlinearities, and using only one localized control moving support. The model deal is derived from well-known reaction–diffusion Gray–Scott when diffusion coefficient first chemical species \(d_u\) tends 0 s...

Managing inter-object dependencies in object-oriented systems is a complex task. Changes of one object often require dependent objects to change accordingly. Making every object explicitly inform every dependent object about its state changes intertwines object interfaces and implementations, thereby hampering system evolution and maintenance. These problems can be overcome by introducing the n...

We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of se...

The simulation of nonlinear components is central to virtual analog simulation. In audio effects, circuit elements often include devices such as diodes and transistors, mostly operating in the strongly regime. Mathematical models are form systems ordinary differential equations (ODEs), traditional integrators, trapezoid midpoint methods, can be employed solvers. These methods fully implicit, re...

We improve the algorithm given in [3]. Through analysing the structural properties of a first order autonomous ODE with a rational solution, we give a polynomial time algorithm to find a rational general solution if it exists.

It often happens that iteration processes used for solving the implicit relations arising in ODE-IVP methods only start to converge rapidly after a certain number of iterations. Fast convergence right from the beginning is particularly important if we want to use so-called step-parallel iteration in which the iteration method is concurrently applied at a number of step points. In this paper, we...