in this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (nsfds). numerical examples confirming then efficiency of schemes, for some differential equations are provided. in order toillustrate the accuracy of the new nsfds, the numerical results are compared with s...

This paper presents a survey of past transformation functions for image registration and introduces a new transformation function for registration of images containing rigid as well as nonrigid regions. Included in the survey are similarity transformation, linear transformation, and nonlinear transformation. Nonlinear transformation itself includes thin-plate splines, radial basis functions, ap...

This paper considers the problem of the stabilization of affine nonlinear control systems. First, we assume that the systems under investigation are of the generalized Byrnes–Isidori normal form. A new way to approximate the center manifold is proposed, which can reduce the error degree of the center manifold approximation. A new matrix product, called the semi-tensor product, is introduced to ...

As an alternative to the rather intensive computations when using the nonlinear traffic flow model METANET in a model-based predictive control context, a piecewise-affine (PWA) approximation of the model is proposed. Here, several model equations amongst which the fundamental diagram are approximated by a PWA function. Some selected methods to determine this approximation are shortly discussed....

Purpose: To investigate the Lie groups of transformations (symmetries) approximately admitted by a finite difference discretization of a nonlinear advection equation on an unstructured mesh. Method: A recently developed technique of " approximate group analysis " is applied to a differential approximation (otherwise referred to as an equivalent differential equation) corresponding to the above ...

Polynomials are very simple mathematical functions which have the flexibility to represent very general nonlinear relationships. Approximation of more complicated functions by polynomials is a basic building block for many numerical techniques. This article considers two distinct but related applications. The first is polynomial regression in which polynomials are used to model a nonlinear rela...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

In the context of a variation of the standard UFL (Uncapacitated Facility Location) problem, but with an objective function that is a separable convex quadratic function of the transportation costs, we present some techniques for improving relaxations of MINLP formulations. We use a disaggregation principal and a strategy of developing model-specific valid inequalities (some nonlinear), which e...

From the point of view of information processing the immune system is a highly parallel and distributed intelligent system which has learning, memory, and associative retrieval capabilities. In this paper we present two immunity-based hybrid learning approaches for function approximation (or regression) problems that involve adjusting the structure and parameters of spatially localized models (...

We construct a new orthonormal basis for L(R), whose elements are angularly integrated ridge functions — orthonormal ridgelets. The new basis functions are in L(R) and so are to be distinguished from the ridge function approximation system called ridgelets by Candès (1997, 1998), as ridge functions are not in L(R). Orthonormal ridgelet expansions have an interesting application in nonlinear app...