The aim of this paper is to construct a new method for solving systems of nonlinear equations. The new method is based on the idea of Gauss-Seidel method, which is a known method for solving systems of linear equations, and considering any equation, in such a system of nonlinear equations, as an equation of one variable.

Statistical properties of the noisy Burgers and KdV-Burgers equations are numerically studied. It is found that shock-like structures appear in the timeaveraged patterns for the case of stepwise fixed boundary conditions. Our results show that the shock structure for the noisy KdV-Burgers equation has an oscillating tail, even for the time averaged pattern. Also, we find that the width of the s...

We demonstrate that the coherence of a noisy or chaotic self-sustained oscillator can be efficiently controlled by the delayed feedback. We develop a theory of this effect, considering noisy systems in the Gaussian approximation. We obtain a closed equation system for the phase diffusion constant and the mean frequency of oscillation. For weak feedback and strong noise, the theory is in good ag...

Camera pose estimation is the problem of determining the position and orientation of an internally calibrated camera from known 3D reference points and their images. We introduce a new polynomial equation system for 4-point pose estimation and apply our symbolicnumeric method to solve it stably and efficiently. In particular, our algorithm can also recognize the points near critical configurati...

In this paper we apply for the rst time a new method for multivariate equation solving which was developed in 18], 19], 20] for complex root determination to the real case. Our main result concerns the problem of nding at least one representative point for each connected component of a real compact and smooth hypersurface. The basic algorithm of 18], 19], 20] yields a new method for symbolicall...

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this...

Here we will consider the problem min f ( ) θ∈Θ θ where, for a given value of θ , we are not able to evaluate analytically or numerically, but must obtain (noisy) estimates of f ( f ( ) θ ) θ using simulation. We will assume for now that the set of possible solutions Θ is uncountably infinite. In particular, suppose that Θ is an interval [ θ θ, θ Θ ] of real numbers. One approach to solving the...

Differential–difference equation; Collocation points; Polynomial solutions Abstract This paper contributes a new matrix method for solving systems of high-order linear differential–difference equations with variable coefficients under given initial conditions. On the basis of the presented approach, the matrix forms of the Euler polynomials and their derivatives are constructed, and then by sub...

The problem of optimal mass transport arises in numerous applications including image registration, mesh generation, reflector design, and astrophysics. One approach to solving this problem is via the Monge-Ampère equation. While recent years have seen much work in the development of numerical methods for solving this equation, very little has been done on the implementation of the transport bo...

‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎ ‎differential equations is considered‎. ‎This technique describes‎ ‎converting of a given fractional Riccati differential equation to a‎ ‎system of nonlinear algebraic equations by using some simple‎ ‎matrices‎. ‎We use fractional derivatives in the Caputo form‎. ‎Convergence analysis of the proposed method is given an...