scholarly journals A novel method for the space and time fractional Bloch-Torrey equations

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 253-258 ◽  
Author(s):  
Esra Akgul
Keyword(s):  
Exact Solution ◽  
Reproducing Kernel ◽  
Kernel Functions ◽  
Efficient Technique ◽  
Series Solutions ◽  
Numerical Example ◽  
Space And Time ◽  
Novel Method

Reproducing kernel technique was implemented to solve the fractional Bloch-Torrey equations. This efficient technique was used via some useful reproducing kernel functions, to obtain approximations to the exact solution in form of series solutions. A numerical example has been presented to prove efficiency of developed technique.

scholarly journals New method for investigating the density-dependent diffusion Nagumo equation

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 143-152 ◽  
Author(s):  
Ali Akgul ◽  
Mir Hashemi ◽  
Mustafa Inc ◽  
Dumitru Baleanu ◽  
Hasib Khan
Keyword(s):  
Exact Solution ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Kernel Functions ◽  
New Method ◽  
Series Solutions ◽  
Powerful Method ◽  
Reproducing Kernel Method ◽  
Density Dependent ◽  
Nagumo Equation

We apply reproducing kernel method to the density-dependent diffusion Nagumo equation. Powerful method has been applied by reproducing kernel functions. The approximations to the exact solution are obtained. In particular, series solutions are obtained. These solutions demonstrate the certainty of the method. The results acquired in this work conceive many attracted behaviors that assure further work on the Nagumo equation.

scholarly journals A novel method for nonlinear singular oscillators

2020 ◽  
pp. 146134842098053
Author(s):  
Ali Akgül ◽  
Hijaz Ahmad ◽  
Yu-Ming Chu ◽  
Phatiphat Thounthong
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Reproducing Kernel Method ◽  
Novel Method ◽  
Relationship Of

The present work deals with a study of a nonlinear singular oscillator. To approximate the frequency–amplitude relationship of the singular oscillator, reproducing kernel method is employed. The approximate solution is compared with the exact solution as well as the results obtained by the He’s frequency–amplitude formulation, to show the effectiveness of the proposed technique for solving the problem.

scholarly journals Museum metabarcoding: A novel method revealing gut helminth communities of small mammals across space and time

2018 ◽  
Vol 48 (13) ◽  
pp. 1061-1070 ◽  
Author(s):  
Stephen E. Greiman ◽  
Joseph A. Cook ◽  
Vasyl V. Tkach ◽  
Eric P. Hoberg ◽  
Damian M. Menning ◽  
...  
Keyword(s):  
Small Mammals ◽  
Space And Time ◽  
Helminth Communities ◽  
Novel Method

scholarly journals Global monopole metric in 2 + 1 dimensions

2019 ◽  
Vol 16 (01) ◽  
pp. 1950006
Author(s):  
S. Habib Mazharimousavi ◽  
M. Halilsoy
Keyword(s):  
Exact Solution ◽  
Cosmological Constant ◽  
Electric Charge ◽  
Radial Distance ◽  
Series Solutions ◽  
Global Monopole ◽  
Negative Cosmological Constant ◽  
Consistent Manner ◽  
Positive Integers

In order to obtain the geometry of a global monopole without cosmological constant and electric charge in [Formula: see text] dimensions, we make use of the broken [Formula: see text] symmetry. In the absence of an exact solution, we determine the series solutions for both the metric and monopole functions in a consistent manner that satisfies all equations in appropriate powers. The new expansion elements are of the form [Formula: see text] for the radial distance [Formula: see text] and positive integers [Formula: see text] and [Formula: see text] constrained by [Formula: see text]. To the lowest order of expansion, we find that in analogy with the negative cosmological constant the geometry of the global monopole acts repulsively, i.e. in the absence of a cosmological constant the global monopole plays at large distances the role of a negative cosmological constant.

scholarly journals Efficient Technique for Facial Image Recognition With Support Vector Machines in 2D Images With Cross-validation in Matlab

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Support Vector Machines ◽  
Cross Validation ◽  
Facial Recognition ◽  
Kernel Functions ◽  
Efficient Technique ◽  
Support Vector ◽  
Facial Image ◽  
Vector Machines ◽  
Validation Technique ◽  
2D Images

This article presented in the context of 2D global facial recognition, using Gabor Wavelet's feature extraction algorithms, and facial recognition Support Vector Machines (SVM), the latter incorporating the kernel functions: linear, cubic and Gaussian. The models generated by these kernels were validated by the cross validation technique through the Matlab application. The objective is to observe the results of facial recognition in each case. An efficient technique is proposed that includes the mentioned algorithms for a database of 2D images. The technique has been processed in its training and testing phases, for the facial image databases FERET [1] and MUCT [2], and the models generated by the technique allowed to perform the tests, whose results achieved a facial recognition of individuals over 96%.

scholarly journals Reliable Iterative Method for solving Volterra - Fredholm Integro Differential Equations

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Samaher Marez
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Iterative Process ◽  
Initial Conditions ◽  
High Accuracy ◽  
Series Solutions ◽  
Math Program ◽  
The Right

  The aim of this paper, a reliable iterative method is presented for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method.  Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibit that this technique has compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

scholarly journals Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bothayna S. H. Kashkari ◽  
Muhammed I. Syam
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Integrodifferential Equation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Integrodifferential Equations ◽  
Reproducing Kernel Method ◽  
Numerical Studies ◽  
Uniformly Convergence ◽  
Present Algorithm

This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.

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