RBF collocation approach to calculate numerically the solution of the nonlinear system of qFDEs

Ghassabzadeh, Fahimeh Akhavan; Tohidi, Emran; Singh, Harendra; Shateyi, Stanford

doi:10.1016/j.jksus.2020.101288

Cited by 5 publications

(2 citation statements)

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“…In Step 1, the global RBF method will be used to solve the problem Equation (31). For the global RBF method, one can refer to [34][35][36][37] for details. Let x = ½x 1 , x 2 , ⋯, x p , x p+1 , ⋯, x M ′, where x 1 , x 2 , ⋯, x p within Ω and x p+1 , ⋯, x M on Γ (Γ is the boundary), and x j = ½x j 1 , x j 2 , ⋯, x j M ′ represents coordinates of the jth node.…”

Section: Two-level Mesh Methods For Integro-differential Equationmentioning

confidence: 99%

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Analysis of Two-Level Mesh Method for Partial Integro-Differential Equation

Tang

Luo

Zhang

et al. 2022

Journal of Function Spaces

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In this paper, we present two-level mesh scheme to solve partial integro-differential equation. The proposed method is based on a finite difference method. For the first step, we use finite difference method in time and global radial basis function (RBF) finite difference (FD) in space. For the second step, we use the finite difference method to solve the proposed problem. This two-level mesh scheme is obtained by combining the radial basis function with finite difference. We prove the stability and convergence of scheme and show that the convergence order is O τ 2 + h 2 , where τ and h are the time step size and space step size, respectively. The results of numerical examples are compared with analytical solutions to show the efficiency of proposed scheme. The numerical results are in good agreement with theoretical ones.

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Section: Two-level Mesh Methods For Integro-differential Equationmentioning

confidence: 99%

“…The coefficients γ k j will be obtained by solving the system of Equation (35). By Equation (33), we can get the approximate solution of u for any point, which will be used in Step 2.…”

Section: Two-level Mesh Methods For Integro-differential Equationmentioning

confidence: 99%