16.920J/SMA 5212 Numerical Methods for PDEs is the stability criterion for the leapfrog time discretization scheme used above Slide 28 EXAMPLE 2 Leapfrog Time Discretization: Stability Diagram The stability diagram for the leapfrog(or any general time discretization scheme in the cplane is Region of Stability Reo) Slide 29 Stability Diagram in the an-plane Alternatively, we can express the stability criterion for the leapfrog time discretization cheme as h Since o<l and o= exp(ie) m(h) nh=isin 0 for stability The stability diagram for the leapfrog time Region of Stability discretization scheme in the Ah-plane would therefore be as shown Re(h) 1816.920J/SMA 5212 Numerical Methods for PDEs 18 is the stability criterion for the leapfrog time discretization scheme used above. Slide 28 EXAMPLE 2 Leapfrog Time Discretization: Stability Diagram The stability diagram for the leapfrog (or any general) time discretization scheme in the σ-plane is Slide 29 Stability Diagram in the λh-plane Alternatively, we can express the stability criterion for the leapfrog time discretization scheme as 1 1 s.t. 1 2 λh σ σ σ ￾ ✁ = − < ✂ ✄ ☎ ✆ Since σ <1 and σ = exp(iθ ) , λh = isinθ for stability. The stability diagram for the leapfrog time discretization scheme in the λh-plane would therefore be as shown: Im(σ ) -1 1 Re(σ ) Region of Stability Re(λh) Im(λh) -1 1 Region of Stability