Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.

Collocation Method with Quintic B-Spline Method for Solving the Hirota equation

Abstract: In the present article, a numerical method is proposed for the numerical solution of the Hirota equation by using collocation method with the quintic B-spline. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L2, L∞ are computed. Two invariants of motion are predestined to determine the conservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is plain to apply

On the Hyers--Ulam--Rassias stability of a generalized mixed type of quartic, cubic, quadratic and additive functional equations in quasi-Banach spaces

Abstract: On the Hyers–Ulam–Rassias stability of a generalized mixed type of quartic, cubic, quadratic and additive functional equations in quasi-Banach spaces Abstract. In this paper, we obtain the general solution and the generalized Hyers–Ulam– Rassias stability of the following functional equation in quasi-Banach spaces f (x + ky) + f (x − ky) = k 2 f (x + y) + k 2 f (x − y) + 2(1 − k 2)f (x) + k 2 (k 2 − 1) 12 (˜ f (2y) − 4 ˜ f (y)) for fixed integers k with k = 0, ±1 where˜f (y) := f (y) + f (−y). The results achieved in this paper are comprehensive such that contain the results in papers obtained by I. [21] and also some other papers.

Numerical solution of full fractional Duffing equations with Cubic-Quintic-Heptic nonlinearities

Abstract: In this article, based on the operational matrix of fractional order integration, we introduce a method for the numerical solution of fractional strongly nonlinear Duffing oscillators with cubic-quintic-heptic nonlinear restoring force and then use it in some cases. For this purpose, concerning the Caputo sense, we implement the block-pulse wavelets matrix of fractional order integration. To reach this aim, we analyse the errors. The approach has been examined by some numerical examples and changes in coefficients as well as in the derivative of the equation too. It is shown that this method works well for all the parameters and order of the fractional derivative. Results indicate the precision and computational performance of the suggested algorithm.

FPGA Gaussian random number generator based on quintic hermite interpolation inversion

Abstract: In this work we present a very accurate floating point FPGA implementation of a Gaussian random number generator (GRNG) based on the inversion method. The inverse Gaussian cumulative distribution function (GCDF-1) is approximated using a quintic degree segment interpolation with Hermite coefficients and an accuracy-adaptative segmentation which divides the GCDF-1 into several non-uniform segments. Our architecture generates simple floating point samples of 32 bits with an accuracy of 20 bits of mantissa, achieving a 185 MHz speed and a throughput of one sample per cycle on a Xilinx Virtex-II FPGA.

Solution of Fourth Order Boundary Value Problems by Numerical Algorithms Based on Nonpolynomial Quintic Splines

Abstract: A family of fourth and second-order accurate numerical schemes is presented for the solution of nonlinear fourth-order boundary-value problems (BVPs) with two-point boundary conditions. Non-polynomial quintic spline functions are applied to construct the numerical algorithms. This approach generalizes nonpolynomial spline algorithms and provides a solution at every point of the range of integration. Two numerical examples are given to illustrate the applicability and efficiency of the reported algorithms.