Table 5 The absolute error for \(\pmb{u(x+\sin(\frac{\pi}{2} t),t)}\) in Example 2
From: A Ritz-Galerkin approximation to the solution of parabolic equation with moving boundaries
( x , t ) | N = 2, M = 2 | N = 2, M = 4 | N = 2, M = 6 |
|---|---|---|---|
(0,0) | 0 | 0 | 0 |
(0.1,0.1) | −1.10 × 10−3 | 8.91 × 10−6 | 2.48 × 10−7 |
(0.2,0.2) | −1.05 × 10−3 | −7.88 × 10−5 | 3.76 × 10−7 |
(0.3,0.3) | 1.87 × 10−3 | −7.79 × 10−5 | −1.83 × 10−6 |
(0.4,0.4) | 5.66 × 10−3 | 1.04 × 10−4 | −5.49 × 10−7 |
(0.5,0.5) | 6.76 × 10−3 | 2.31 × 10−4 | 3.37 × 10−6 |
(0.6,0.6) | 3.35 × 10−3 | 7.52 × 10−5 | 9.43 × 10−7 |
(0.7,0.7) | −2.45 × 10−3 | −1.85 × 10−4 | −3.68 × 10−6 |
(0.8,0.8) | −5.56 × 10−3 | −1.56 × 10−4 | 1.55 × 10−7 |
(0.9,0.9) | −2.82 × 10−3 | 6.30 × 10−5 | 1.34 × 10−6 |
(1,1) | 0 | 0 | 0 |