Numerical Approximation for Fractional Neutron Transport Equation

Fractional neutron transport equation reflects the anomalous processes in nuclear reactor. In this paper, we will construct fully discrete methods for type of fractional with Riesz derivative, where generalized WENO5 scheme is used spatial direction and Runge–Kutta schemes are adopted temporal direction. The linear stabilities different stages order ERK discussed detailed. Numerical examples show combinations forward Euler/two-stage, second-order unstable three-stage, third-order method stable can maintain sharp transitions discontinuous problem, its convergence reaches fifth smooth boundary condition.