Related papers: On finding bifurcations for non-variational ellipt…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…
Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to a separation of time-scales, often evolve towards a lower dimensional manifold $M$. We introduce an approach to locate saddle points…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation method with global basis functions. It is known to have exponentional convergence for interpolation problems. We descretize nonlinear elliptic PDEs by the MQ…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
Sampling equation method is presented to look for exact solutions of nonlinear differential equations. Application of this approach to one of the extensive chaos model is considered. Exact solutions of this model in travelling wave are…
We study main bifurcations of multidimensional diffeomorphisms having a non-transversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation diagram for single-round periodic orbits lying entirely in a…
In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…
In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by…
A novel method to derive stationary solutions of the Vlasov-Maxwell system is established. This method is based on the assumption that the deviation of the velocity distribution from the Maxwell-Boltzmann distribution can be expanded by the…
Based on G. Lan's accelerated gradient sliding and general relation between the smoothness and strong convexity parameters of function under Legendre transformation we show that under rather general conditions the best known bounds for…
We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory,…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions. Our approach depends on local and…
The exponential B-spline basis function set is used to develop a collocation method for some initial boundary value problems (IBVPs) to the Gardner equation. The Gardner equation has two nonlinear terms, namely quadratic and cubic ones. The…
In this work, we investigate the inverse problem of determining a quasilinear term appearing in a nonlinear elliptic equation from the measurement of the conormal derivative on the boundary. This problem arises in several practical…
In this paper, we propose two parallel extragradient - viscosity methods for finding a particular element in the common solution set of a system of equilibrium problems and finitely many fixed point problems. This particular point is the…
Analytical expressions for coordinates of stationary points and conditions for their existence in the ABC flow are received. The type of the stationary points is shown analytically to be saddle-node. Exact expressions for eigenvalues and…
Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search…