Numerical investigation of the accuracy and stability properties of the flux relaxation method

The computational properties of the flux relaxation method is studied on the example of a numerical solution of the quasi linear heat conduction equation. The accuracy of the obtained solution is analyzed depending on the step of difference grid and relaxation parameter for schemes of the first and second order approximation in time. It was experimentally confirmed that both of these variants of the method have the stability condition of the Courant type. It is concluded that on not the coarsest grids, increasing the time approximation order does not give advantages either in terms of the accuracy of the solution or in the sense of the algorithm stability.