scholarly journals Chebyshev neural network model with linear and nonlinear active functions

2016 ◽  
Vol 5 (3) ◽  
pp. 182
Author(s):  
Sarkhosh Seddighi Chaharborj ◽  
Yaghoub Mahmoudi
Keyword(s):  
Neural Network ◽  
Neural Network Model ◽  
Initial Value Problems ◽  
High Accuracy ◽  
Numerical Results ◽  
Initial Value ◽  
Linear Ordinary Differential Equations ◽  
Chebyshev Neural Network ◽  
Active Function ◽  
Linear And Nonlinear

In this paper the second order non-linear ordinary differential equations of Lane-Emden type as singular initial value problems using Chebyshev Neural Network (ChNN) with linear and nonlinear active functions has been studied. Active functions as, \(\texttt{F(z)=z}, \texttt{sinh(x)}, \texttt{tanh(z)}\) are considered to find the numerical results with high accuracy. Numerical results from Chebyshev Neural Network shows that linear active function has more accuracy and is more convenient compare to other functions.

scholarly journals Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28
Author(s):  
Jiang Zhu ◽  
Dongmei Liu
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Second Order ◽  
Dynamic Equations ◽  
Maximum Principles ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Approximation Theorems ◽  
Construction Techniques ◽  
Linear And Nonlinear

Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.

Study on Rapid Archival Technology of Bullets Based on Graph Convolutional Neural Network

2021 ◽  
Author(s):  
Shi-bo Pan ◽  
Di-lin Pan ◽  
Nan Pan ◽  
Xiao Ye ◽  
Miaohan Zhang
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Neural Network Model ◽  
Dynamic Time Warping ◽  
Large Scale ◽  
Line Graph ◽  
High Accuracy ◽  
Time Warping ◽  
Large Numbers ◽  
Dynamic Time

Traditional gun archiving methods are mostly carried out through bullets’ physics or photography, which are inefficient and difficult to trace, and cannot meet the needs of large-scale archiving. Aiming at such problems, a rapid archival technology of bullets based on graph convolutional neural network has been studied and developed. First, the spot laser is used to take the circle points of the bullet rifling traces. The obtained data is filtered and noise-reduced to make the corresponding line graph, and then the dynamic time warping (DTW) algorithm convolutional neural network model is used to perform the processing on the processed data. Not only is similarity matched, the rapid matching of the rifling of the bullet is also accomplished. Comparison of experimental results shows that this technology has the advantages of rapid archiving and high accuracy. Furthermore, it can be carried out in large numbers at the same time, and is more suitable for practical promotion and application.

Regularity properties of Schrödinger equations in vector-valued spaces and applications

2019 ◽  
Vol 31 (1) ◽  
pp. 149-166
Author(s):  
Veli Shakhmurov
Keyword(s):  
Initial Value Problems ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Initial Value ◽  
Physical Systems ◽  
Regularity Properties ◽  
The Cauchy Problem ◽  
Linear And Nonlinear ◽  
Vector Valued Function ◽  
Vector Valued

Abstract In this paper, regularity properties and Strichartz type estimates for solutions of the Cauchy problem for linear and nonlinear abstract Schrödinger equations in vector-valued function spaces are obtained. The equation includes a linear operator A defined in a Banach space E, in which by choosing E and A, we can obtain numerous classes of initial value problems for Schrödinger equations, which occur in a wide variety of physical systems.

A P-STABLE EIGHTEENTH-ORDER SIX-STEP METHOD FOR PERIODIC INITIAL VALUE PROBLEMS

2007 ◽  
Vol 18 (03) ◽  
pp. 419-431 ◽  
Author(s):  
CHUNFENG WANG ◽  
ZHONGCHENG WANG
Keyword(s):  
Initial Value Problems ◽  
Numerical Results ◽  
New Method ◽  
Initial Value ◽  
Step Method ◽  
Periodic Initial Value Problems

In this paper we present a new kind of P-stable eighteenth-order six-step method for periodic initial-value problems. We add the fourth derivatives to our previous P-stable six-step method to increase the accuracy. We apply two classes of well-known problems to our new method and compare it with the previous methods. The numerical results show that the new method is much more stable, accurate and efficient than the previous methods.

A P-stable complete in phase Obrechkoff trigonometric fitted method for periodic initial-value problems

1993 ◽  
Vol 441 (1912) ◽  
pp. 283-289 ◽  
Keyword(s):  
Initial Value Problems ◽  
Numerical Results ◽  
New Method ◽  
Phase Lag ◽  
Initial Value ◽  
Periodic Initial Value Problems

In this paper we derive a P-stable trigonometric fitted Obrechkoff method with phase-lag (frequency distortion) infinity. It is easy to see, from numerical results presented, that the new method is much more accurate than previous methods.

An Efficient Neural Network Model with Taylor Series-Based Data Pre-Processing for Stock Price Forecast

2013 ◽  
Vol 284-287 ◽  
pp. 3020-3024
Author(s):  
Jung Bin Li ◽  
Chien Ho Wu
Keyword(s):  
Neural Network ◽  
Empirical Study ◽  
Neural Network Model ◽  
Taylor Series ◽  
Stock Price ◽  
Input Data ◽  
Back Propagation ◽  
Back Propagation Neural Network ◽  
High Accuracy ◽  
Price Forecast

This study adopts popular back-propagation neural network to make one-period-ahead prediction of the stock price. A model based on Taylor series by using both fundamental and technical indicators EPS and MACD as input data is built for an empirical study. Leading Taiwanese companies in non-hi-tech industry such as Formosa Plastics, Yieh Phui Steel, Evergreen Marine, and Chang Hwa Bank are picked as targets to analyze their reasonable prices and moving trends. The performance of this model shows remarkable return and high accuracy in making long/short strategies.

scholarly journals Collocation polynomial neural forms and domain fragmentation for solving initial value problems

2021 ◽  
Author(s):  
Toni Schneidereit ◽  
Michael Breuß
Keyword(s):  
Neural Network ◽  
Differential Equations ◽  
Initial Value Problems ◽  
Feedforward Neural Networks ◽  
Computational Domain ◽  
Initial Value ◽  
Trial Solution ◽  
Grid Points ◽  
Set Up ◽  
Network Approaches

AbstractSeveral neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance, one may include them directly in the cost function. Used within the corresponding neural network, the trial solutions define the so-called neural form. Such neural forms represent general, flexible tools by which one may solve various differential equations. In this article, we consider time-dependent initial value problems, which require to set up the neural form framework adequately. The neural forms presented up to now in the literature for such a setting can be considered as first-order polynomials. In this work, we propose to extend the polynomial order of the neural forms. The novel collocation-type construction includes several feedforward neural networks, one for each order. Additionally, we propose the fragmentation of the computational domain into subdomains. The neural forms are solved on each subdomain, whereas the interfacing grid points overlap in order to provide initial values over the whole fragmentation. We illustrate in experiments that the combination of collocation neural forms of higher order and the domain fragmentation allows to solve initial value problems over large domains with high accuracy and reliability.

Sign in / Sign up

Export Citation Format

Share Document