MOTIVATION Transcription regulation is a fundamental process in biology, and it is important to model the dynamic behavior of gene regulation networks. Many approaches have been proposed to specify the network structure. However, finding the network connectivity is not sufficient to understand the network dynamics. Instead, one needs to model the regulation reactions, usually with a set of ordi...

Hidden symmetries of ordinary differential equations (ODEs) are studied with nonlocal group generators. General forms are given for an exponential nonlocal group generator of an ODE that is reduced from a higher-order ODE, which is expressed in canonical variables and which is invariant under a two-parameter Lie group. The nonlocal group generator identifies a type I hidden symmetry. Type II hi...

We establish the equivalence of free piston and delta shock, for one-space-dimensional pressureless compressible Euler equations. The shock appearing in singular Riemann problem is exactly that may move freely forward or backward a straight tube, driven by flows on two sides it tube. This result not only helps to understand physics somewhat mysterious shocks, but also provides way reduce fluid-...

In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE ...

In this paper, we introduce SODES (Stepwise Ordinary Differential Equations Solver) a new solver for (ODE). can optionally provide the solution displaying all steps needed to obtain it. This way, is an important tool not only researchers who need solving ODE but also constitutes teaching and learning process of ODE. has been developed using programming with Computer Algebra System (CAS). Specif...

Interval numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs) compute bounds that contain the solution of an IVP for an ODE. This paper develops and studies an interval method for computing bounds on the solution of a linear ODE. Our method is based on enclosing the terms in the formula for the closed form solution using Taylor series and various interv...

The study of dynamical models of HIV infection, based on a system of nonlinear ordinary differential equations (ODE), has considerably improved the knowledge of its pathogenesis. While the first models used simplified ODE systems and analyzed each patient separately, recent works dealt with inference in non-simplified models borrowing strength from the whole sample. The complexity of these mode...

We consider the problem of estimating parameters and unobserved trajectories in nonlinear ordinary differential equations (ODEs) from noisy and partially observed data. We focus on a class of statespace models defined from the integration of the differential equation in the evolution equation. Within a Bayesian framework, we derive a nonsequential estimation procedure that infers the parameters...

We put forward a new method for the solution of eigenvalue problems for (systems of) ordinary differential equations, where our main focus is on eigenvalue problems for singular Schrödinger equations arising, for example, in electronic structure computations. Here, the generation of the starting values for the computation of eigenvalues of higher index is a critical issue. Our approach comprise...

In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE ...