Numerical approximation of the nonlinear time-fractional telegraph equation arising in neutron transport

Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A.

http://hdl.handle.net/10400.22/18095

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Authors

Nikan, O.

Avazzadeh, Z.

Tenreiro Machado, J. A.

Abstract(s)

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(τ3−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.