Reproducing kernel Hilbert space method for nonlinear boundary-value problems

2018 ◽  
Vol 41 (18) ◽  
pp. 9142-9151 ◽  
Author(s):  
Esra Karatas Akgül
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Space Method

Multiplicity results by shooting reproducing kernel Hilbert space method for the catalytic reaction in a flat particle

2018 ◽  
Vol 17 (02) ◽  
pp. 1850020 ◽  
Author(s):  
Babak Azarnavid ◽  
Elyas Shivanian ◽  
Kourosh Parand ◽  
Soudabeh Nikmanesh
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Reproducing Kernel ◽  
High Efficiency ◽  
Reproducing Kernel Hilbert Space ◽  
Boundary Value ◽  
Well Performance ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

In this paper, a model of simultaneous mass and heat transfer within a porous catalyst in a flat particle is considered. A new modification of the shooting reproducing kernel Hilbert space (SRKHS) method is proposed, which is also capable of handling the system of nonlinear boundary value problems by employing Newtons method. The proposed method is a well-performance technique in both predicting and calculating multiple solutions of the nonlinear boundary value problems. Applying the SRKHS method shows that the mentioned model might admit multiple stationary solutions (unique, dual or triple solutions) depending on the values of the parameters of the model. Furthermore, the convergence of the method is proved and some numerical tests reveal the high efficiency of this new version of SRKHS method.

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.

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