scholarly journals A novel method for the solution of Blasius equation in semi-infinite domains

2017 ◽  
Vol 7 (2) ◽  
pp. 225-233 ◽  
Author(s):  
Ali Akgül
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Analytic Solutions ◽  
Reproducing Kernel Method ◽  
Infinite Domains ◽  
Blasius Equation ◽  
Novel Method

Many known methods fail in the attempt to get analytic solutions of Blasius-type equations. In this work, we apply the reproducing kernel method for ivestigating Blasius equations with two different boundary conditions in semi-infinite domains. Convergence analysis of the reproducing kernel method is given. The numerical approximations are presented and compared with some other techniques, Howarth's numerical solution and Runge-Kutta Fehlberg method.

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 Solving non-local fractical heat equations based on the reproducing kernel method

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 711-716
Author(s):  
Xiuying Li ◽  
Boying Wu
Keyword(s):  
Boundary Conditions ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Nonlocal Conditions ◽  
Heat Equations ◽  
Reproducing Kernel Method ◽  
Local Boundary ◽  
Non Local ◽  
Reproducing Kernel Theory ◽  
Kernel Theory

In this paper, a numerical method is proposed for 1-D fractional heat equations subject to non-local boundary conditions. The reproducing kernel satisfying nonlocal conditions is constructed and reproducing kernel theory is applied to solve the considered problem. A numerical example is given to show the effectiveness of the method.

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.

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