On Reproducing Kernel Spaces, J Unitary Matrix Functions, Interpolation and Displacement Rank

1989 ◽  
pp. 665-731
Author(s):  
Harry Dym
Keyword(s):  
Reproducing Kernel ◽  
Unitary Matrix ◽  
Matrix Functions ◽  
Reproducing Kernel Spaces ◽  
Displacement Rank

scholarly journals Numerical Solution of a Class of Time-Fractional Order Diffusion Equations in a New Reproducing Kernel Space

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaoli Zhang ◽  
Haolu Zhang ◽  
Lina Jia ◽  
Yulan Wang ◽  
Wei Zhang
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Diffusion Equations ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Reproducing Kernel Method ◽  
Reproducing Kernel Spaces ◽  
Methods Numerical

In this paper, we structure some new reproducing kernel spaces based on Jacobi polynomial and give a numerical solution of a class of time fractional order diffusion equations using piecewise reproducing kernel method (RKM). Compared with other methods, numerical results show the reliability of the present method.

scholarly journals Numerical Solution of Fractional Order Burgers’ Equation with Dirichlet and Neumann Boundary Conditions by Reproducing Kernel Method

2020 ◽  
Vol 4 (2) ◽  
pp. 27 ◽  
Author(s):  
Onur Saldır ◽  
Mehmet Giyas Sakar ◽  
Fevzi Erdogan
Keyword(s):  
Fractional Order ◽  
Reproducing Kernel ◽  
Burgers Equation ◽  
Kernel Method ◽  
Reproducing Kernel Hilbert Space ◽  
Neumann Boundary ◽  
Kernel Functions ◽  
Iterative Approach ◽  
Reproducing Kernel Method ◽  
Reproducing Kernel Spaces

In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms. Then an iterative approach is constructed by using kernel functions. The convergence of this approach and its error estimates are given. The numerical algorithm of the method is presented. Furthermore, numerical outcomes are shown with tables and graphics for some examples. These outcomes demonstrate that the proposed method is convenient and effective.

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