Numerical solution of PDEs (intro)
General · Mathematics
Study notes
Q: One explicit step for heat equation u_t = u_xx, h = 0.25, k = 0.02, u = [0,1,1,0]. r = k/h² = 0.02/0.0625 = 0.32 ≤ 0.5: stable ✓. FTCS: uⱼⁿ⁺¹ = uⱼ+r(uⱼ₊₁-2uⱼ+uⱼ₋₁). Interior j=1: 1+0.32(1-2+0) = 1-0.32 = 0.68. Interior j=2: 1+0.32(0-2+1) = 1-0.32 = 0.68. New: [0, 0.68, 0.68, 0] (boundaries fixed!)! (Heat spreads!)