Discrete L1 and errors for P and W at T = 2 under grid refinement, together with estimated convergence orders p and regression coefficients R2.

Here Nx denotes the number of grid points and the time step. Errors decrease monotonically with Nx, and observed orders cluster near 1 in all norms, consistent with the scheme’s first-order truncation error. Slight deviations from exactly 1 arise from boundary/discretization effects. A conservative CFL number C = 0.005 was used here to suppress other artifacts. High R2 values confirm excellent log–log linearity.