Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate

2019 ◽  
Vol 38 (4) ◽  
Author(s):  
Onur Saldır ◽  
Mehmet Giyas Sakar ◽  
Fevzi Erdogan
Keyword(s):  
Error Estimate ◽  
Numerical Solution ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Kawahara Equation ◽  
Reproducing Kernel 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 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 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 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.

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