A Fast High-Order Nonpolynomial Spline Method for Nonlinear Time-Fractional Telegraph Model for Neutron Transport in a Nuclear Reactor

Abstract

The aim of the present study is to develop a fast high-order method for a nonlinear time-fractional telegraph model for neutron transport in a nuclear reactor. The discretization of the model involves the utilization of a fast Alikhanov formula for the time-fractional derivative and a high-order nonpolynomial spline scheme for the spatial variable. The proposed algorithm is computationally efficient with computational cost of (Formula presented.) and a storage requirement of (Formula presented.), where (Formula presented.) and (Formula presented.) represent the total number of grids in space and time, respectively. The stability and convergence of the developed method are established using the discrete energy approach in the (Formula presented.) norm. It is proved that the developed method converges with an order of (Formula presented.) where (Formula presented.) and (Formula presented.) represent the step sizes in time and space, respectively. The term (Formula presented.) represents the approximation error introduced by the fast sum-of-exponentials approximation. The numerical simulations validate the theoretical convergence outcome and showcase the effectiveness of the proposed approach. © 2025 John Wiley & Sons Ltd.