2-stage explicit total variation diminishing preserving Runge-

In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Runge-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ODEs. Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities

Initial value problem, Method of Line, Total-variation-diminishing, Runge-Kutta methods