scholarly journals Reproducing kernel Hilbert space method for the solutions of generalized Kuramoto–Sivashinsky equation

2019 ◽  
Vol 13 (1) ◽  
pp. 661-669 ◽  
Author(s):  
Ali Akgül ◽  
Ebenezer Bonyah
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Sivashinsky Equation ◽  
Space Method

scholarly journals Reproducing kernel functions for the generalized Kuramoto-Sivashinsky equation

2018 ◽  
Vol 22 ◽  
pp. 01028
Author(s):  
Ali Akgül ◽  
Esra Karatas Akgül ◽  
Sahin Korhan ◽  
Mustafa Inc
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Kernel Functions ◽  
Sivashinsky Equation ◽  
Space Method

Reproducing kernel functions are obtained for the solution of generalized Kuramoto–Sivashinsky (GKS) equation in this paper. These reproducing kernel functions are valuable in the reproducing kernel Hilbert space method. They will be useful for interested researchers.

scholarly journals Solving a Class of Singular Fifth-Order Boundary Value Problems Using Reproducing Kernel Hilbert Space Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yulan Wang ◽  
Shuai Lu ◽  
Fugui Tan ◽  
Mingjing Du ◽  
Hao Yu
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Reproducing Kernel Space ◽  
Finite Section ◽  
Finite Section Method ◽  
Fifth Order ◽  
Space Method

We use the reproducing kernel Hilbert space method to solve the fifth-order boundary value problems. The exact solution to the fifth-order boundary value problems is obtained in reproducing kernel space. The approximate solution is given by using an iterative method and the finite section method. The present method reveals to be more effective and convenient compared with the other methods.

scholarly journals Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Banan Maayah ◽  
Samia Bushnaq ◽  
Shaher Momani ◽  
Omar Abu Arqub
Keyword(s):  
Hilbert Space ◽  
Series Solution ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Nonlinear Oscillators ◽  
Strongly Nonlinear ◽  
Runge Kutta Method ◽  
Strongly Nonlinear Oscillators ◽  
Space Method ◽  
Good Agreement

A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.

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