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

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.

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Numerical solution of nonlinear Volterra integro-differential equations of fractional order by the reproducing kernel method

Applied Mathematical Modelling ◽

10.1016/j.apm.2015.03.053 ◽

2015 ◽

Vol 39 (16) ◽

pp. 4871-4876 ◽

Cited By ~ 33

Author(s):

Wei Jiang ◽

Tian Tian

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Fractional Order ◽

Reproducing Kernel ◽

Kernel Method ◽

Reproducing Kernel Method

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

Fractal and Fractional ◽

10.3390/fractalfract4020027 ◽

2020 ◽

Vol 4 (2) ◽

pp. 27 ◽

Cited By ~ 1

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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The piecewise reproducing kernel method for the time variable fractional order advection-reaction-diffusion equations

Thermal Science ◽

10.2298/tsci200302021d ◽

2021 ◽

pp. 21-21

Author(s):

Dan-Dan Dai ◽

Ting-Ting Ban ◽

Yu-Lan Wang ◽

Wei Zhang

Keyword(s):

Fractional Order ◽

Legendre Polynomials ◽

Reproducing Kernel ◽

Kernel Method ◽

Reaction Diffusion ◽

Time Variable ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Variable Order ◽

Reproducing Kernel Method

This paper structures some new reproductive kernel spaces based on Legendre polynomials to solve time variable order fractional advection-reaction-diffusion equations. Some examples are given to show the effectiveness and reliability of the method.

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The Combined Reproducing Kernel Method and Taylor Series for Solving Weakly Singular Fredholm Integral Equations

International Journal of Advances in Applied Sciences ◽

10.11591/ijaas.v5.i3.pp109-117 ◽

2016 ◽

Vol 5 (3) ◽

pp. 109

Author(s):

Azizallah Alvandi ◽

Mahmoud Paripour

Keyword(s):

Integral Equations ◽

Taylor Series ◽

Reproducing Kernel ◽

Kernel Method ◽

Fredholm Integral Equations ◽

Kernel Space ◽

Reproducing Kernel Space ◽

Reproducing Kernel Method ◽

Weakly Singular ◽

Reproducing Kernel Function

<p>In this paper, a numerical method is proposed for solving weakly singular Fredholm integral equations in Hilbert reproducing kernel space (RKHS). The Taylor series is used to remove singularity and reproducing kernel function are used as a basis. The effectiveness and stability of the numerical scheme is illustrated through two numerical examples.</p>

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