Non-dissipative time-integration schemes for the linear advection equation

We discuss an application of the class of non-dissipative methods, introduced recently in Chawla and Al-Zanaidi [1], for the time-integration of the linear advection equation: u(t) + a(x,t)u(x) = 0. Since spatial discretization affects, often adversely, the property of non-dissipativity, to fully realize the non-dissipativity of these rules, in the present investigation we consider their application to the linear advection equation combined with the method of characteristics. Numerical experiments confirm the non-dissipativity of these time-integration schemes for the important instances of problems in which the initial condition is a pulse with jump discontinuities or steep fronts.