1. Recall the matrix A, in the finite-difference solution of the boundary value problem discussed CO...

Transcribed Image Text:

1. Recall the matrix A, in the finite-difference solution of the boundary value problem discussed COŚ Th, p(BCS) in class (steady state heat conduction). It was stated in class that p(B₁) 1+sin Th cos² th, p(B.) = 1-sin Th where h is the mesh size. Use MATLAB to plot p(B) versus h for 0<h≤ 1/2 for each method. Include all three methods on the same plot and label each curve. Plot a small symbol on each curve at h= 1/2, 1/4, 1/8, 1/16. a) Explain why the plot shows that all three methods converge for any mesh size 0 <h ≤ 1/2. b) Explain how to tell from the plot which method converges fastest and which converges slowest. 1. Recall the matrix A, in the finite-difference solution of the boundary value problem discussed COŚ Th, p(BCS) in class (steady state heat conduction). It was stated in class that p(B₁) 1+sin Th cos² th, p(B.) = 1-sin Th where h is the mesh size. Use MATLAB to plot p(B) versus h for 0<h≤ 1/2 for each method. Include all three methods on the same plot and label each curve. Plot a small symbol on each curve at h= 1/2, 1/4, 1/8, 1/16. a) Explain why the plot shows that all three methods converge for any mesh size 0 <h ≤ 1/2. b) Explain how to tell from the plot which method converges fastest and which converges slowest.

Answer rating: 100% (QA)

To plot B versus h for each method and analyze their convergence we first need to define the functio... View the full answer