scholarly journals A modified reproducing kernel method for a time-fractional telegraph equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1575-1580 ◽  
Author(s):  
Yulan Wang ◽  
Mingjing Du ◽  
Chaolu Temuer
Keyword(s):  
Numerical Solution ◽  
Present Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Telegraph Equation ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Fractional Telegraph Equation

The aim of this work is to obtain a numerical solution of a time-fractional telegraph equation by a modified reproducing kernel method. Two numerical examples are given to show that the present method overcomes the drawback of the traditional reproducing kernel method and it is an easy and effective method.

scholarly journals The Solution of a Class of Singularly Perturbed Two-Point Boundary Value Problems by the Iterative Reproducing Kernel Method

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Zhiyuan Li ◽  
YuLan Wang ◽  
Fugui Tan ◽  
Xiaohui Wan ◽  
Tingfang Nie
Keyword(s):  
Singular Perturbation ◽  
Boundary Layers ◽  
Present Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Perturbation Problems

In (Wang et al., 2011), we give an iterative reproducing kernel method (IRKM). The main contribution of this paper is to use an IRKM (Wang et al., 2011), in singular perturbation problems with boundary layers. Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate that the method is simple and effective.

scholarly journals Explicit Solution of Telegraph Equation Based on Reproducing Kernel Method

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Mustafa Inc ◽  
Ali Akgül ◽  
Adem Kiliçman
Keyword(s):  
Exact Solution ◽  
Explicit Solution ◽  
Reproducing Kernel ◽  
Initial Conditions ◽  
Kernel Method ◽  
Telegraph Equation ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Reproducing Kernel Theory ◽  
Kernel Theory

We propose a reproducing kernel method for solving the telegraph equation with initial conditions based on the reproducing kernel theory. The exact solution is represented in the form of series, and some numerical examples have been studied in order to demonstrate the validity and applicability of the technique. The method shows that the implement seems easy and produces accurate results.

scholarly journals Numerical Solutions of the Second-Order One-Dimensional Telegraph Equation Based on Reproducing Kernel Hilbert Space Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Mustafa Inc ◽  
Ali Akgül ◽  
Adem Kılıçman
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Kernel Method ◽  
Reproducing Kernel Hilbert Space ◽  
Telegraph Equation ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Reproducing Kernel Theory ◽  
Space Method

We investigate the effectiveness of reproducing kernel method (RKM) in solving partial differential equations. We propose a reproducing kernel method for solving the telegraph equation with initial and boundary conditions based on reproducing kernel theory. Its exact solution is represented in the form of a series in reproducing kernel Hilbert space. Some numerical examples are given in order to demonstrate the accuracy of this method. The results obtained from this method are compared with the exact solutions and other methods. Results of numerical examples show that this method is simple, effective, and easy to use.

Investigation of Numerical Solution for Fourth-Order Nonlocal Problem by the Reproducing Kernel Method

2011 ◽  
Author(s):  
Kemal Özen ◽  
Kamil Oruçoğlu ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Fourth Order ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Nonlocal Problem ◽  
Reproducing Kernel Method

scholarly journals A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Mustafa Inc ◽  
Ali Akgül ◽  
Adem Kiliçman
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Kdv Equation ◽  
Reproducing Kernel Hilbert Space ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
The Kdv Equation ◽  
Novel Method ◽  
Reproducing Kernel Theory

We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective.

scholarly journals Numerical Solution of a Class of Time-Fractional Order Diffusion Equations in a New Reproducing Kernel Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaoli Zhang ◽  
Haolu Zhang ◽  
Lina Jia ◽  
Yulan Wang ◽  
Wei Zhang
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Diffusion Equations ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Reproducing Kernel Method ◽  
Reproducing Kernel Spaces ◽  
Methods Numerical

In this paper, we structure some new reproducing kernel spaces based on Jacobi polynomial and give a numerical solution of a class of time fractional order diffusion equations using piecewise reproducing kernel method (RKM). Compared with other methods, numerical results show the reliability of the present method.

scholarly journals Reproducing kernel method for the numerical solution of the Brinkman–Forchheimer momentum equation

2017 ◽  
Vol 311 ◽  
pp. 262-271 ◽  
Author(s):  
S. Abbasbandy ◽  
R.A. Van Gorder ◽  
P. Bakhtiari
Keyword(s):  
Numerical Solution ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Momentum Equation ◽  
Reproducing Kernel Method

scholarly journals A high order approach for nonlinear Volterra-Hammerstein integral equations

2021 ◽  
Vol 7 (1) ◽  
pp. 1460-1469
Author(s):  
Jian Zhang ◽  
◽  
Jinjiao Hou ◽  
Jing Niu ◽  
Ruifeng Xie ◽  
...  
Keyword(s):  
Integral Equation ◽  
Nonlinear Integral Equation ◽  
Homotopy Perturbation Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Linear Equations ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Hammerstein Integral Equations ◽  
Homotopy Perturbation

<abstract><p>Here a scheme for solving the nonlinear integral equation of Volterra-Hammerstein type is given. We combine the related theories of homotopy perturbation method (HPM) with the simplified reproducing kernel method (SRKM). The nonlinear system can be transformed into linear equations by utilizing HPM. Based on the SRKM, we can solve these linear equations. Furthermore, we discuss convergence and error analysis of the HPM-SRKM. Finally, the feasibility of this method is verified by numerical examples.</p></abstract>

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