Theory and Modern Applications
Table 4 Comparisons by the maximum errors to Example 1 for \(h=1/19\) (i.e., \(m-1=18=6K\), \(K=3\))
From: A new parallel algorithm for solving parabolic equations
Methods | r | t = 0.2 | t = 0.4 | t = 0.6 | t = 0.8 |
|---|---|---|---|---|---|
Algorithm 1 | 0.36 | 3.5539e−4 | 4.8387e−4 | 5.9795e−4 | 7.3131e−4 |
ASC-N scheme [6] | 4.7468e−4 | 7.1743e−4 | 1.0705e−3 | 1.5969e−3 | |
Algorithm 1 | 0.72 | 5.7866e−4 | 7.8813e−4 | 9.7397e−4 | 1.1912e−3 |
ASC-N scheme [6] | 7.3439e−4 | 1.1100e−3 | 1.6563e−3 | 2.4709e−3 | |
Algorithm 1 | 1.08 | 7.9673e−4 | 1.0815e−3 | 1.3381e−3 | 1.6382e−3 |
ASC-N scheme [6] | 1.1764e−3 | 1.7767e−3 | 2.1187e−3 | 3.9468e−3 | |
Algorithm 1 | 1.45 | 1.0066e−3 | 1.3715e−3 | 1.6949e−3 | 2.0729e−3 |
ASC-N scheme [6] | 1.0999e−3 | 1.6591e−3 | 2.4754e−3 | 3.6929e−3 | |
Algorithm 1 | 1.80 | 1.2153e−3 | 1.6560e−3 | 2.0465e−3 | 2.5029e−3 |
ASC-N scheme [6] | 1.2843e−3 | 1.9356e−3 | 2.8880e−3 | 4.3084e−3 |