相关论文: Method of variation of parameters revisited

We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…

An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic…

Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…

The method and the formula of variation of constants for ordinary differential equations (ODEs) is a fundamental tool to analyze the dynamics of an ODE near an equilibrium. It is natural to expect that such a formula works for delay…

A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…

Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…

Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial…

In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed…

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…

The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

Onsager's variational principle (OVP) provides us with a systematic way to derive dynamical equations for various soft matter and active matter. By reformulating the Onsager-Machlup variational principle (OMVP), which is a time-global…

The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g.,…

In this study, we give the variation of parameters method from a different viewpoint for the Nth order inhomogeneous linear ordinary difference equations with constant coefficient by means of delta exponential function . Advantage of this…

In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for…

We have developed a variational perturbation theory based on the Liouville-Neumann equation, which enables one to systematically compute the perturbative correction terms to the variationally determined wave functions of the time-dependent…

The variable separated ODE method is extended by choosing the additional variable separated equation as the general elliptic equation. More exact traveling wave solutions of nonlinear equations are obtained by using the method of comparison…

Using min-max inequality we investigate the existence of solutions and thier dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle…