16.920J/SMA 5212 Numerical Methods for PDEs intensive/expensive compared to the multiplication/ addition operations of explicit schemes SUMMARY Stability Analysis of Parabolic PDE Uncoupling the set Integrating each equation in the uncoupled set modal equation Re-coupling the results to form final solution Use of modal equation to analyze the stability ldah)l<l Explicit time discretization versus Implicit time discretization Reference Numerical Computation of Internal and External Flows, Vol I lI by C Hirsch, 1992, Wiley series16.920J/SMA 5212 Numerical Methods for PDEs 31 intensive/expensive compared to the multiplication/ addition operations of explicit schemes. Slide 48 SUMMARY • Stability Analysis of Parabolic PDE ￾ Uncoupling the set. ￾ Integrating each equation in the uncoupled set → modal equation. ￾ Re-coupling the results to form final solution. • Use of modal equation to analyze the stability |σ(λh)| < 1. • Explicit time discretization versus Implicit time discretization. Slide 49 Reference: Numerical Computation of Internal and External Flows, Vol I & II by C. Hirsch, 1992, Wiley Series