A five-point thirty-two convergence order derivative-free iterative method to find simple roots of non-linear equations is constructed. Six function evaluations are performed achieve optimal 26-1 = 32 conjectured by Kung and Traub [1]. Secant approximation the derivative computed around initial guess. High attained constructing polynomials quotients for functional values.

This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper by the author and Koornwinder in 2012. Here, an approximation of the Weyl or Riemann–Liouville fractional derivative is considered by replacing the n-th derivative...

The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of the world, (ii) it constitutes an excellent model for the receptive fields of simple cells in the primary visual cortex and (iii) it is covariant under affi...

We propose a generic procedure to raise the approximation order of multivariate approximation schemes using supplementary derivative data. The procedure applies to all schemes that reproduce polynomials to a certain degree, including most common types of (quasi-) interpolation and moving least-squares. For an approximation scheme of orderm and a dataset that provides n supplementary orders of d...

The goal of this article is to develop local discontinuous Galerkin (LDG) schemes for solving a time fractional equation describing the ultrasonic wave in homogeneous isotropic porous material. Two novel semi-discrete LDG are designed considered model. constructed by splitting original model into coupled system. first scheme follows traditional method second-order space derivative. second one s...

terracing is an operator that is applied to potential field data to produce regions of constant field amplitude that are separated by sharp boundaries. magnetic data are usually transformed into pseudo-gravity data (baranov, 1957) prior to the application of terracing. the objective of terracing is ‘to recast potential field maps into a geologic map like format’ (cordell and mccafferty 1989). t...

Spline curves are very prominent in the mathematics due to their simple construction, accuracy of assessment and ability approximate complicated structures into interactive curved designs. A spline is a smooth piece-wise polynomial function. The primary goal this study use extended cubic B-spline (ExCuBS) functions with new second order derivative approximation obtain numerical solution weakly ...