Two-steps Lagrange polynomial interpolation: numerical scheme

2021 ◽  
pp. 11-112
Author(s):  
Abdon Atangana ◽  
Seda İğret Araz
Keyword(s):  
Numerical Scheme ◽  
Polynomial Interpolation ◽  
Lagrange Polynomial

scholarly journals Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 641
Author(s):  
Wang Huang ◽  
Jianjun Yang ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Pihua Wen
Keyword(s):  
Finite Element Method ◽  
Numerical Solutions ◽  
Shape Function ◽  
Polynomial Interpolation ◽  
Finite Domain ◽  
Mapping Technique ◽  
Lagrange Polynomial ◽  
Block Method ◽  
Nonlinear Characteristics ◽  
Typical Material

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

scholarly journals Improvement of LTE Downlink System Performances Using the Lagrange Polynomial Interpolation

2014 ◽  
Vol 6 (5) ◽  
pp. 129-143
Author(s):  
Mallouki Nasreddine ◽  
Nsiri Bechir ◽  
Walid Hakimi ◽  
Mahmoud Ammar
Keyword(s):  
Polynomial Interpolation ◽  
Lagrange Polynomial ◽  
Downlink System

Highly accurate technique for studying some chaotic models described by ABC-fractional differential equations of variable-order

2020 ◽  
pp. 2150018
Author(s):  
M. M. Khader ◽  
Ibrahim Al-Dayel
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Numerical Technique ◽  
Variable Order ◽  
Lagrange Polynomial ◽  
Efficient Tool ◽  
Fractional Differential ◽  
The Given

The propose of this paper is to introduce and investigate a highly accurate technique for solving the fractional Logistic and Ricatti differential equations of variable-order. We consider these models with the most common nonsingular Atangana–Baleanu–Caputo (ABC) fractional derivative which depends on the Mittag–Leffler kernel. The proposed numerical technique is based upon the fundamental theorem of the fractional calculus as well as the Lagrange polynomial interpolation. We satisfy the efficiency and the accuracy of the given procedure; and study the effect of the variation of the fractional-order [Formula: see text] on the behavior of the solutions due to the presence of ABC-operator by evaluating the solution with different values of [Formula: see text]. The results show that the given procedure is an easy and efficient tool to investigate the solution for such models. We compare the numerical solutions with the exact solution, thereby showing excellent agreement which we have found by applying the ABC-derivatives. We observe the chaotic solutions with some fractional-variable-order functions.

APPLICATION OF THE POLYNOMIAL INTERPOLATION METHOD FOR DETERMINING PERFORMANCE CHARACTERISTICS OF A DIESEL ENGINE

2014 ◽  
Vol 21 (1) ◽  
pp. 157-168 ◽  
Author(s):  
Tomasz Stoeck ◽  
Karol Franciszek Abramek
Keyword(s):  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Sufficient Accuracy ◽  
Performance Characteristics ◽  
Combustion Engines ◽  
Lagrange Polynomial ◽  
Minimum Number ◽  
Mathematical Equations ◽  
Bench Testing ◽  
Engine Type

Abstract The article shows the methodology and calculation procedures based on Lagrange polynomial interpolation which were used to determine standard performance characteristics of the Polish production engine, type ANDORIA 4CTi90-1BE6. They allow to simplify the experimental research by maintaining a minimum number of measurement points and estimating the remaining data in an analytical way. The methods presented are convenient when it comes to the practical side because they eliminate the need for exploration of mathematical equations describing the various curves, which can be cumbersome and time consuming in the case of nonautomated accounts. The results of analysis were applied to actual experimental results, indicating sufficient accuracy of the resulting approximations. As a result, procedures may be used in bench testing of a similar profile, especially with repeated cycles of the experiment, such as optimization of operating parameters of combustion engines.

Identification of emitter sources in the aspect of their fractal features

2013 ◽  
Vol 61 (3) ◽  
pp. 623-628 ◽  
Author(s):  
J. Dudczyk ◽  
A. Kawalec
Keyword(s):  
Linear Regression ◽  
Polynomial Interpolation ◽  
Original Signal ◽  
Lagrange Polynomial ◽  
Specific Kind ◽  
Distinctive Features ◽  
Measurement Function ◽  
Change Measure ◽  
Specific Emitter Identification ◽  
Radar Signals

Abstract This article presents the procedure of identification radar emitter sources with the trace distinctive features of original signal with the use of fractal features. It is a specific kind of identification called Specific Emitter Identification, where as a result of using transformations, which change measure points, a transformation attractor was received. The use of linear regression and the Lagrange polynomial interpolation resulted in the estimation of the measurement function. The method analysing properties of the measurement function which has been suggested by the authors caused the extraction of two additional distinctive features. These features extended the vector of basic radar signals’ parameters. The extended vector of radar signals’ features made it possible to identify the copy of radar emitter source.

Sign in / Sign up

Export Citation Format

Share Document