Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way...

This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation (PIDE) with a weakly singular kernel. Cubic trigonometric B-spline (CTBS) functions are used interpolation in both methods. The first method is CTBS based collocation which reduces PIDE to an algebraic tridiagonal system linear equations. other differentia...

A method for generating an interpolation closed G arc spline on a given closed point set is presented. For the odd case, i.e. when the number of the given points is odd, this paper disproves the traditional opinion that there is only one closed G arc spline interpolating the given points. In fact, the number of the resultant closed G arc splines fulfilling the interpolation condition for the od...

B-spline scaling functions and wavelets have found wide applicability in many scientific and practical problems thanks to their unique properties. They show considerably better results in comparison to other wavelets, and they are used as well in mathematical approximations, signal processing, image compression, etc. But only the first four wavelets from this family were mathematically formulat...

Many papers describe techniques for evaluating spline curves and surfaces. While each paper provides some theoretical or empirical evidence with which to compare techniques, there exist few global comparisons Peters94]. Also, papers describing particular algorithms often provide few details, making implementation of the technique presented diicult or impossible. This report attempts to illumina...

In this paper it is presented another method to determine the coefficients in B-spline interpolation. The problem is resolved in the context of generalized spline interpolation. To determine the coefficients from the input samples is first step for performing the interpolation. The operation is done by using also the values of the second derivative for the input signal. The coefficients are use...

Quartic-Spline Collocation Methods for Fourth-Order Two-Point Boundary Value Problems Ying Zhu Master of Science Graduate Department of Computer Science University of Toronto 2001 This thesis presents numerical methods for the solution of general linear fourth-order boundary value problems in one dimension. The methods are based on quartic splines, that is, piecewise quartic polynomials with C3...

quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the or...