In this work we consider a simple, approximate, tending toward exact, solution of the system of two usual Lotka-Volterra differential equations. Given solution is obtained by an iterative method. In any finite approximation order of this solution, exponents of the corresponding Lotka-Volterra variables have simple, time polynomial form. When approximation order tends to infinity obtained approx...

A submanifold in space forms is isoparametric if the normal bundle is flat and principal curvatures along any parallel normal fields are constant. We study the mean curvature flow with initial data an isoparametric submanifold in Euclidean space and sphere. We show that the mean curvature flow preserves the isoparametric condition, develops singularities in finite time, and converges in finite ...

This paper studies an exchange economy with indivisibilities. Our main goal is to see if a price system can function well in an economy (e.g., an economy with complementary preferences) that does not have a Walrasian equilibrium. We study the price adjustment processes governed by the Euler iterative scheme. We show that in an economy that has a Walrasian equilibrium, our price adjustment proce...

In this manuscript we present a p-th degree immersed finite element method for solving boundary value problems with discontinuous coefficients. In this method, interface jump conditions are employed in the finite element basis functions, and the mesh does not have to be aligned with coefficient discontinuity. We show that under h refinement the immersed finite element solution converges to the ...

We consider solutions of a one dimensional stochastic differential equations that explode in finite time. We prove that, under suitable hypotheses, the explosion time converges almost surely to the one of the ODE governed by the drift term when the diffusion coefficient approaches zero.

In [20] a symmetric interior penalty discontinuous Galerkin (DG) method was presented for the time-dependent wave equation. In particular, optimal a-priori error bounds in the energy norm and the L-norm were derived for the semi-discrete formulation. Here the error analysis is extended to the fully discrete numerical scheme, when a centered second-order finite difference approximation (“leapfro...

In this paper, finite-time cluster synchronization (FTCS) in networks of nonidentical coupled dynamical systems is addressed by introducing a discontinuous interaction rule. This rule overcomes the effect heterogeneous dynamics among nodes. It proven that with proper coupling gain, system converges into kernal space graph Laplacian matrix finite time. Then sufficient conditions for FTCS are pro...

A nonlinear finite-time sliding mode control is proposed in this paper for the governing of complex hydroelectric systems with finite/fixed setting time. The method derived from stability and theories. finite settling time calculated bounded, not depending on initial conditions system. solution trajectory controlled system can reach manifold a fixed time, regardless values. Based Lyapunov theor...

We present an iterative algorithm for computing values of optimal stopping problems for one-dimensional diffusions on finite time intervals. The method is based on a time discretisation of the initial model and a construction of discretised analogues of the associated integral equation for the value function. The proposed iterative procedure converges in a finite number of steps and delivers in...