Related papers: A dynamical system based on projection operator fo…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
In our previous work, numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the…
We propose a new kind of stochastic absolute value equations involving absolute values of variables. By utilizing an equivalence relation to stochastic bilinear program, we investigate the expected value formulation for the proposed…
A projection operator technique for solution of relativistic wave equation on non-compact group has been proposed. This technique was applied to the construction of wave equations for charged vector boson in a potential field. The equations…
In this paper we report a few examples of algebraically solvable dynamical systems characterized by 2 coupled Ordinary Differential Equations which read as follows: x_n = P(n) (x1, x2) , n = 1, 2 , with P(n) (x1, x2) specific polynomials of…
This paper proposes an efficient numerical method based on second-order cone programming (SOCP) to solve dynamic optimal transport (DOT) problems with quadratic cost on staggered grid discretization. By properly reformulating discretized…
We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…
A fixed-time stable dynamical system for solving the extended vertical linear complementarity problem (EVLCP) is developed. The system is based on the reformulation of EVLCP as a special case of a new kind of generalized absolute value…
In this paper, we propose two projection dynamical systems for solving inverse quasi-variational inequality problems in finite-dimensional Hilbert spaces-one ensuring finite-time stability and the other guaranteeing fixed-time stability. We…
By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the…
Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…
We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on $S^1$, whichn in turn is related to the stability algebra of Virasoro orbit. Using Darboux…
A recursion operator is constructed for a new integrable system of coupled Korteweg - de Vries equations by the method of gauge-invariant description of zero-curvature representations. This second-order recursion operator is characterized…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
Usually, the systems of partial differential equations (PDEs) are discovered from observational data in the single vector equation form. However, this approach restricts the application to the real cases, where, for example, the form of the…
A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
Projection-based control (PBC) systems have significant engineering impact and receive considerable scientific attention. To properly describe closed-loop PBC systems, extensions of classical projected dynamical systems are needed, because…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…