scholarly journals Numerical Solution of Seventh Order Boundary Value Problems Using the Reproducing Kernel Space

2014 ◽  
Vol 7 (4) ◽  
pp. 892-896
Author(s):  
Ghazala Akram ◽  
Hamood Ur Rehman
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Seventh Order

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.

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.

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