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 New Numerical Method for Solving Tenth Order Boundary Value Problems

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 245 ◽  
Author(s):  
Ali Akgül ◽  
Esra Karatas Akgül ◽  
Dumitru Baleanu ◽  
Mustafa Inc
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problems ◽  
Numerical Method ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Kernel Functions ◽  
Numerical Results ◽  
Space Method

In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate solutions. We obtain very efficient results by this method. We show our numerical results by tables.

scholarly journals Reproducing kernel functions for linear tenth-order boundary value problems

2018 ◽  
Vol 22 ◽  
pp. 01027
Author(s):  
Ali Akgül ◽  
Esra Karatas Akgül ◽  
Baris Orcan ◽  
Mustafa Inc
Keyword(s):  
Hilbert Space ◽  
Numerical Methods ◽  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Kernel Functions ◽  
Space Method ◽  
Higher Order Differential Equations

Higher order differential equations have always been an onerous problem to investigate for the mathematicians and engineers. Different numerical methods were applied to get numerical approximations of such problems. This paper gives some reproducing kernel functions to find approximate solutions of the tenth-order boundary value problems (BVPs). These reproducing kernel functions are very important in the reproducing kernel Hilbert space method.

scholarly journals A Novel Method for Solutions of Fourth-Order Fractional Boundary Value Problems

2019 ◽  
Vol 3 (2) ◽  
pp. 33 ◽  
Author(s):  
Ali Akgül ◽  
Esra Karatas Akgül
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Novel Method ◽  
Fractional Boundary Value Problems ◽  
Space Method

In this paper, we find the solutions of fourth order fractional boundary value problems by using the reproducing kernel Hilbert space method. Firstly, the reproducing kernel Hilbert space method is introduced and then the method is applied to this kind problems. The experiments are discussed and the approximate solutions are obtained to be more correct compared to the other obtained results in the literature.

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