Beam and Warming scheme

In this an efficient factored algorithm is obtained by evaluating the spatial cross derivatives explicitly.

[1] The delta form of the equation produced has the advantageous property of stability (if existing) independent of the size of the time step.

[4] Under the condition of shock wave, dissipation term is required for nonlinear hyperbolic equations such as this.

If only the stable solution is required, then in the equation to the right hand side a second-order smoothing term is added on the implicit layer.

This scheme is produced by combining the trapezoidal formula, linearization, factoring, Padt spatial differencing, the homogeneous property of the flux vectors (where applicable), and hybrid spatial differencing and is most suitable for nonlinear systems in conservation-law form.

ADI algorithm retains the order of accuracy and the steady-state property while reducing the bandwidth of the system of equations.

[5] Stability of the equation is The order of Truncation error is The result is smooth with considerable overshoot (that does not grow much with time).