scholarly journals A parallel Numerical Algorithm For Solving Some Fractional Integral Equations

2019 ◽  
Vol 32 (1) ◽  
pp. 184
Author(s):  
Khalid Mindeel Mohammed
Keyword(s):  
Neural Network ◽  
Integral Equations ◽  
Numerical Algorithm ◽  
Fractional Integral ◽  
High Accuracy ◽  
Numerical Results ◽  
New Method ◽  
Training Algorithm ◽  
Numerical Examples ◽  
Fractional Equations

In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1st and 2nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

scholarly journals Numerical Algorithm to Solve a Class of Variable Order Fractional Integral-Differential Equation Based on Chebyshev Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Kangwen Sun ◽  
Ming Zhu
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Numerical Algorithm ◽  
Chebyshev Polynomials ◽  
Fractional Integral ◽  
Numerical Solutions ◽  
Variable Order ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Integral Differential Equation

The purpose of this paper is to study the Chebyshev polynomials for the solution of a class of variable order fractional integral-differential equation. The properties of Chebyshev polynomials together with the four kinds of operational matrixes of Chebyshev polynomials are used to reduce the problem to the solution of a system of algebraic equations. By solving the algebraic equations, the numerical solutions are acquired. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach and the results have been compared with the exact solution.

scholarly journals Increasing of Thermal Images Resolution Using Deep Learning Neural Networks

2021 ◽  
Vol 25 (3) ◽  
pp. 31-35
Author(s):  
Piotr Więcek ◽  
Dominik Sankowski
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Execution Time ◽  
High Accuracy ◽  
New Method ◽  
Residual Network ◽  
Thermal Images ◽  
The Neural Network

The article presents a new algorithm for increasing the resolution of thermal images. For this purpose, the residual network was integrated with the Kernel-Sharing Atrous Convolution (KSAC) image sub-sampling module. A significant reduction in the algorithm’s complexity and shortening the execution time while maintaining high accuracy were achieved. The neural network has been implemented in the PyTorch environment. The results of the proposed new method of increasing the resolution of thermal images with sizes 32 × 24, 160 × 120 and 640 × 480 for scales up to 6 are presented.

Application of Hybrid Subgroup Decomposition Method to Gas Cooled Thermal Reactor Problem

2014 ◽  
Author(s):  
Saam Yasseri ◽  
Farzad Rahnema
Keyword(s):  
Transport Equation ◽  
Computational Efficiency ◽  
Decomposition Method ◽  
High Accuracy ◽  
Numerical Results ◽  
New Method ◽  
Thermal Reactor ◽  
Problem Characteristic ◽  
Group Transport ◽  
Subgroup Decomposition

In this paper, a newly developed hybrid subgroup decomposition method is tested in a 1D problem characteristic of gas cooled thermal reactors (GCR). The new method couples an efficient coarse-group eigenvalue calculation with a set of fine-group transport source iterations to unfold the fine-group flux. It is shown that the new method reproduces the fine-group transport solution by iteratively solving the coarse-group quasi transport equation. The numerical results demonstrate that the new method applied to 1D GCR problem is capable of achieving high accuracy while gaining computational efficiency up to 5 times compared to direct fine-group transport calculations.

scholarly journals Comparison of the Orthogonal Polynomial Solutions for Fractional Integral Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 59
Author(s):  
Ayşegül Daşcıoğlu ◽  
Serpil Salınan
Keyword(s):  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Integral Equations ◽  
Collocation Method ◽  
Fractional Integral ◽  
The Other ◽  
Numerical Examples ◽  
Polynomial Solutions

In this paper, a collocation method based on the orthogonal polynomials is presented to solve the fractional integral equations. Six numerical examples are given to illustrate the method. The results are compared with the other methods in the literature, and the results obtained by different kinds of polynomials are compared.

scholarly journals Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc-Gaussian Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. H. Bhrawy ◽  
M. M. Tharwat ◽  
A. Al-Fhaid
Keyword(s):  
Error Analysis ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Transmission Conditions ◽  
Numerical Results ◽  
New Method ◽  
Dirac System ◽  
Sinc Method ◽  
Dirac Systems ◽  
Gaussian Method

The eigenvalues of a discontinuous regular Dirac systems with transmission conditions at the point of discontinuity are computed using the sinc-Gaussian method. The error analysis of this method for solving discontinuous regular Dirac system is discussed. It shows that the error decays exponentially in terms of the number of involved samples. Therefore, the accuracy of the new method is higher than the classical sinc-method. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented. Comparisons with the classical sinc-method are given.

scholarly journals Numerical solution of linear stochastic Volterra integral equations via new basis functions

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5959-5966
Author(s):  
Tofigh Cheraghi ◽  
Morteza Khodabin ◽  
Reza Ezzati
Keyword(s):  
Linear System ◽  
Numerical Solution ◽  
Integral Equations ◽  
Orthogonal Basis ◽  
Volterra Integral Equations ◽  
Basis Functions ◽  
New Method ◽  
Algebraic Equations ◽  
Numerical Examples

In this article, we use a new method based on orthogonal basis functions for the numerical solution of stochastic Volterra integral equations of the second kind (SVIE). By using this method, a SVIE can be reduced to a linear system of algebraic equations. Finally, to show the efficiency of the proposed method, we give two numerical examples.

scholarly journals Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Abdon Atangana ◽  
Necdet Bildik
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Fractional Integral ◽  
Numerical Results ◽  
Uniqueness Of The Solution ◽  
Picard Method ◽  
Rule Method

This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.

An Investigation of Interpolation Scheme Based on Indirect Radial Basis Neural Networks

2012 ◽  
Vol 226-228 ◽  
pp. 2181-2188
Author(s):  
Hai Tao Sun
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
High Accuracy ◽  
Numerical Results ◽  
Interpolation Scheme ◽  
Radial Basis Neural Network ◽  
Radial Basis Neural Networks ◽  
Radial Basis ◽  
Different Order ◽  
Methods Numerical

An indirect radial basis neural network (IRBNN) is proposed for improving the accuracy of the approximated functions. The IRBNN is constructed by new prompted functions generated from the Nth order derivative of the approximated function. In this way, high accuracy derivatives in different order can be obtained, so that more accuracy of the numerical results would be given while the IRBNN is employed for creating approximated functions in numerical methods. Numerical results through applications in elasticity show the effectiveness and accuracy of the IRBNN method.

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