scholarly journals A comparison of various basis functions based on meshless local Petrov-Galerkin method for linear stability of circular jet

2013 ◽  
Vol 17 (5) ◽  
pp. 1329-1335
Author(s):  
Qing He ◽  
Mingliang Xie
Keyword(s):  
Vector Field ◽  
Linear Stability ◽  
Basis Function ◽  
Degrees Of Freedom ◽  
Basis Functions ◽  
Axial Component ◽  
Continuum Equation ◽  
Perturbation Vector ◽  
Galerkin Spectral Method ◽  
Chebyshev Functions

Various basis functions based on Fourier-Chebyshev Petrov-Galerkin spectral method are described for computation of temporal linear stability of a circular jet. Basis functions presented here are exponentially mapped Chebyshev functions. There is a linear dependence between the components of the perturbation vector field, and there are only two degrees of freedom for the perturbation continuum equation. According to the principle of permutation and combination, the basis function has three basic forms, i. e., the radial, azimuthal or axial component, respectively. The results show that three eigenvalues for various cases are consistent, but there is a preferable basis function for numerical computation.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

Lateral Stability Analysis for Car-Trailer Combinations

2016 ◽  
Author(s):  
Eungkil Lee ◽  
Tao Sun ◽  
Yuping He
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Parametric Study ◽  
Degrees Of Freedom ◽  
Linear Quadratic Regulator ◽  
Lateral Stability ◽  
Linear Quadratic ◽  
Lqr Control ◽  
Ct System

This paper presents a parametric study of linear lateral stability of a car-trailer (CT) combination in order to examine the fidelity, complexity, and applicability for control algorithm development for CT systems. Using MATLAB software, a linear yaw-roll model with 5 degrees of freedom (DOF) is developed to represent the CT combination. In the case of linear stability analysis, a parametric study was carried out using eigenvalue analysis based on a linear yaw-roll CT model with varying parameters. Built upon the linear stability analysis, an active trailer differential braking (ATDB) controller was designed for the CT system using the linear quadratic regulator (LQR) technique. The simulation study presented in this paper shows the effectiveness of the proposed LQR control design and the influence of different trailer parameters.

scholarly journals Broadband Adaptive RCS Computation through Characteristic Basis Function Method

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Guohua Wang ◽  
Yufa Sun
Keyword(s):  
Cross Section ◽  
Basis Function ◽  
Function Method ◽  
High Accuracy ◽  
Wide Frequency Range ◽  
Singular Value ◽  
Basis Functions ◽  
Frequency Range ◽  
Arbitrary Frequency ◽  
Value Decomposition

A broadband radar cross section (RCS) calculation approach is proposed based on the characteristic basis function method (CBFM). In the proposed approach, the desired arbitrary frequency band is adaptively divided into multiple subband in consideration of the characteristic basis functions (CBFs) number, which can reduce the universal characteristic basis functions (UCBFs) numbers after singular value decomposition (SVD) procedure at lower subfrequency band. Then, the desired RCS data can be obtained by splicing the RCS data in each subfrequency band. Numerical results demonstrate that the proposed method achieve a high accuracy and efficiency over a wide frequency range.

scholarly journals Accurate radial basis functions technique for competitive and efficient solutions of non-linear Black-Scholes equations

2020 ◽  
Vol 20 (4) ◽  
pp. 60-83
Author(s):  
Vinícius Magalhães Pinto Marques ◽  
Gisele Tessari Santos ◽  
Mauri Fortes
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Efficient Solutions ◽  
Basis Functions ◽  
Adaptive Scheme ◽  
Call Options ◽  
Black Scholes ◽  
Non Linear ◽  
Radial Basis ◽  
Complex Models

ABSTRACTObjective: This article aims to solve the non-linear Black Scholes (BS) equation for European call options using Radial Basis Function (RBF) Multi-Quadratic (MQ) Method.Methodology / Approach: This work uses the MQ RBF method applied to the solution of two complex models of nonlinear BS equation for prices of European call options with modified volatility. Linear BS models are also solved to visualize the effects of modified volatility.  Additionally, an adaptive scheme is implemented in time based on the Runge-Kutta-Fehlberg (RKF) method.

scholarly journals A New Improved Penalty Avoiding Rational Policy Making Algorithm for Keepaway with Continuous State Spaces

2009 ◽  
Vol 13 (6) ◽  
pp. 675-682 ◽  
Author(s):  
Takuji Watanabe ◽  
◽  
Kazuteru Miyazaki ◽  
Hiroaki Kobayashi ◽  
◽  
...  
Keyword(s):  
Basis Function ◽  
Function Approximation ◽  
Policy Making ◽  
Basis Functions ◽  
State Spaces ◽  
Soccer Game ◽  
Continuous State ◽  
Current Input ◽  
Multiagent Environments ◽  
Parp 1

The penalty avoiding rational policy making algorithm (PARP) [1] previously improved to save memory and cope with uncertainty, i.e., IPARP [2], requires that states be discretized in real environments with continuous state spaces, using function approximation or some other method. Especially, in PARP, a method that discretizes state using a basis functions is known [3]. Because this creates a new basis function based on the current input and its next observation, however, an unsuitable basis function may be generated in some asynchronous multiagent environments. We therefore propose a uniform basis function and range extent of the basis function is estimated before learning. We show the effectiveness of our proposal using a soccer game task called “Keepaway.”

scholarly journals Orthogonal Functions Solving Linear functional Differential EquationsUsing Chebyshev Polynomial

2008 ◽  
Vol 5 (1) ◽  
pp. 143-148 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Function Approximation ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Least Square ◽  
Orthogonal Functions ◽  
Functional Differential ◽  
Approximated Evaluation ◽  
Chebyshev Functions

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

scholarly journals The Conical Radial Basis Function for Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
J. Zhang ◽  
F. Z. Wang ◽  
E. R. Hou
Keyword(s):  
Radial Basis Function ◽  
Boundary Value Problems ◽  
Basis Function ◽  
Boundary Value ◽  
Computational Cost ◽  
Basis Functions ◽  
Simple Scheme ◽  
Collocation Points ◽  
Radial Basis ◽  
Radial Basis Function Method

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.

Differential Evolution-Based Optimization of Kernel Parameters in Radial Basis Function Networks for Classification

2013 ◽  
Vol 4 (1) ◽  
pp. 56-80 ◽  
Author(s):  
Ch. Sanjeev Kumar Dash ◽  
Ajit Kumar Behera ◽  
Satchidananda Dehuri ◽  
Sung-Bae Cho
Keyword(s):  
Neural Networks ◽  
Differential Evolution ◽  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Basis Functions ◽  
Second Phase ◽  
Rbf Neural Networks ◽  
Radial Basis ◽  
Two Phases

In this paper a two phases learning algorithm with a modified kernel for radial basis function neural networks is proposed for classification. In phase one a new meta-heuristic approach differential evolution is used to reveal the parameters of the modified kernel. The second phase focuses on optimization of weights for learning the networks. Further, a predefined set of basis functions is taken for empirical analysis of which basis function is better for which kind of domain. The simulation result shows that the proposed learning mechanism is evidently producing better classification accuracy vis-à-vis radial basis function neural networks (RBFNs) and genetic algorithm-radial basis function (GA-RBF) neural networks.

Multilevel RBF collocation method for the fourth-order thin plate problem

2020 ◽  
pp. 2050079
Author(s):  
Lanling Ding ◽  
Zhiyong Liu ◽  
Qiuyan Xu
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Radial Basis Functions ◽  
Thin Plate ◽  
Fourth Order ◽  
Basis Function ◽  
Research Method ◽  
Meshfree Method ◽  
Basis Functions ◽  
Radial Basis

The radial basis functions meshfree method is a research method for thin plate problem which has gradually developed into a more mature meshfree method. It includes finite element, radial basis functions meshfree collocation method, etc. In this paper, we introduce the multilevel radial basis function collocation method for the fourth-order thin plate problem. We use nonsymmetric Kansa multilevel radial basis function collocation method to solve the fourth-order thin plate problem. Two numerical examples based on Wendland’s [Formula: see text] and [Formula: see text] functions are given to examine that the convergence of the multilevel radial basis function collocation method which is good for solving the fourth-order thin plate problem.

Ultra-wideband characteristic basis function method merging the secondary level characteristic basis functions for rapid computation of wideband radar cross section problems from conducting targets

2020 ◽  
pp. 1-10
Author(s):  
Zhong-Gen Wang ◽  
Jun-Wen Mu ◽  
Wen-Yan Nie
Keyword(s):  
Basis Function ◽  
Function Method ◽  
Secondary Level ◽  
Singular Value ◽  
Basis Functions ◽  
Ultra Wideband ◽  
Scattering Problems ◽  
Wideband Radar ◽  
Value Decomposition ◽  
A Current

In this paper, a merged ultra-wideband characteristic basis function method (MUCBFM) is presented for high-precision analysis of wideband scattering problems. Unlike existing singular value decomposition (SVD) enhanced improved ultra-wideband characteristic basis function method (SVD-IUCBFM), the MUCBFM reduces the number of characteristic basis functions (CBFs) necessary to express a current distribution. This reduction is achieved by combining primary CBFs (PCBFs) with the secondary level CBFs (SCBFs) to form a single merged ultra-wideband characteristic basis function (MUCBF). As the MUCBF incorporates the effects of PCBFs and SCBFs, the accuracy does not change significantly compared to that obtained by the SVD-IUCBFM. Furthermore, the efficiencies of constructing the CBFs and filling the reduced matrix are improved. Numerical examples verify and demonstrate that the proposed method is credible both in terms of accuracy and efficiency.

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