1. Homework 3
Q1) Build a finite-difference solver for: with initial condition:
Q1a) use Heun’s RK3 time integrator
Q1b) use the 4th order central difference in space (periodic domain)
Q1c) perform a stability analysis to determine maximum allowable time-step
Q1d) Fix a small dt and perform an experimental dx convergence analysis based on the error at time t=9 – to estimate the solution order of accuracy in dx
Q1e) Fix a small dx and perform an experimental dt convergence analysis based on the error at time t=9 – to estimate the solution order of accuracy in dt
Q1f) estimate the accuracy order of the solution in dt and dx (use results from Q1d and Q1e)
Q1g) extra credit: set up an adaptive time-stepping using the Cash-Karp RK 6 step, 5th order scheme to keep the local truncation error from time stepping bounded by a tolerance.
Q1h) extra credit: repeat Q1a-Q1f with the 6th order central difference scheme in space and Jameson-Schmit-Turkel in time
CAAM 452 Spring 2006