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• W3127534953 endingPage "105755" @default.
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• W3127534953 abstract "• The time-fractional telegraph model as a useful description of the neutron transport process is generated. • A new hybrid scheme based LRBF-FD method is formulated to approximate the time-fractional telegraph model. • The LRBF-FD method useful for complex domains with acceptable accuracy was proposed. • The stability and convergence are examined using the energy method. This paper focusses on the numerical solution of the nonlinear time-fractional telegraph equation formulated in the Caputo sense. This model is a useful description of the neutron transport process inside the core of a nuclear reactor. The proposed method approximates the unknown solution with the help of two main stages. At a first stage, a semi-discrete algorithm is obtained by means of a difference approach with the accuracy O ( τ 3 − β ) , where 1 < β < 2 is the fractional-order derivative. At a second stage, a full-discretization is obtained by an efficient augmented local radial basis function finite difference (LRBF-FD). This method approximates the derivatives of an unknown function at a given point named as center, based on the finite difference at each local-support domain, instead of applying the entire set of points. The technique produces a sparse matrix system, reduces the computational effort and avoids the ill-conditioning derived from the global collocation. The unconditional stability and convergence of the time-discretized formulation are demonstrated and confirmed numerically. The numerical results highlight the accuracy and the validity of the method." @default.
• W3127534953 created "2021-02-15" @default.
• W3127534953 creator A5015962889 @default.
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• W3127534953 date "2021-08-01" @default.
• W3127534953 modified "2023-10-03" @default.
• W3127534953 title "Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport" @default.
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• W3127534953 doi "https://doi.org/10.1016/j.cnsns.2021.105755" @default.
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