Homotopy deform method for reproducing kernel space for nonlinear boundary value problems

Pramana ◽  
2016 ◽  
Vol 87 (4) ◽  
Author(s):  
MIN-QIANG XU ◽  
YING-ZHEN LIN
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Kernel Space ◽  
Nonlinear Boundary Value Problems ◽  
Reproducing Kernel Space ◽  
Nonlinear Boundary Value

scholarly journals Solutions of a Class of Sixth Order Boundary Value Problems Using the Reproducing Kernel Space

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ghazala Akram ◽  
Hamood Ur Rehman
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Kernel Functions ◽  
Sixth Order ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Computational Point ◽  
Nonlinear Boundary Value

The approximate solution to a class of sixth order boundary value problems is obtained using the reproducing kernel space method. The numerical procedure is applied on linear and nonlinear boundary value problems. The approach provides the solution in terms of a convergent series with easily computable components. The present method is simple from the computational point of view, resulting in speed and accuracy significant improvements in scientific and engineering applications.It was observed that the errors in absolute values are better than compared (Che Hussin and Kiliçman (2011) and, Noor and Mahyud-Din (2008), Wazwaz (2001), Pandey (2012)).Furthermore, the nonlinear boundary value problem for the integrodifferential equation has been investigated arising in chemical engineering, underground water flow and population dynamics, and other fields of physics and mathematical chemistry. The performance of reproducing kernel functions is shown to be very encouraging by experimental results.

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.

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