A posteriori analysis: error estimation for the eighth order boundary value problems in reproducing Kernel space

2016 ◽  
Vol 73 (2) ◽  
pp. 391-406 ◽  
Author(s):  
Taher Lotfi ◽  
Mehdi Rashidi ◽  
Katauoun Mahdiani
Keyword(s):  
Boundary Value Problems ◽  
Error Estimation ◽  
Reproducing Kernel ◽  
A Posteriori ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Eighth Order ◽  
Analysis Error ◽  
Posteriori Analysis ◽  
A Posteriori Analysis

scholarly journals Fuzzy reproducing kernel space method for solving fuzzy boundary value problems

2019 ◽  
Vol 13 (2) ◽  
pp. 97-103
Author(s):  
N. Gholami ◽  
T. Allahviranloo ◽  
S. Abbasbandy ◽  
N. Karamikabir
Keyword(s):  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Boundary Value ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Fuzzy Boundary Value Problems ◽  
Fuzzy Boundary ◽  
Space Method

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.

Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Jiang ◽  
Zhong Chen ◽  
Ning Hu ◽  
Yali Chen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Reproducing Kernel ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Orthonormal Bases ◽  
Fractional Differential

AbstractIn recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.

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