Theory and Modern Applications
Table 3 The absolute errors and relative errors of numerical solutions to Example 1 for \(h=1/25\) (i.e., \(m-1=24=6K\), \(K=4\))
From: A new parallel algorithm for solving parabolic equations
\(x_{j}\) | Algorithm 1 (t = 0.2) | Algorithm 1 (t = 0.4) | Algorithm 1 (t = 0.8) | |||
|---|---|---|---|---|---|---|
A. E. | R. E. | A. E. | R. E. | A. E. | R. E. | |
0.04 | 0.5579e−4 | 9.0292e−3 | 0.7499e−4 | 9.9277e−3 | 1.1317e−4 | 1.0041e−2 |
0.12 | 1.6391e−4 | 9.0313e−3 | 2.2031e−4 | 9.9298e−3 | 3.3247e−4 | 1.0043e−2 |
0.24 | 2.7890e−4 | 8.2703e−3 | 3.7803e−4 | 9.1694e−3 | 5.7102e−4 | 0.9283e−2 |
0.36 | 3.5674e−4 | 8.0054e−3 | 4.8512e−4 | 8.9048e−3 | 7.3305e−4 | 0.9018e−2 |
0.48 | 3.8737e−4 | 7.8818e−3 | 5.2760e−4 | 8.7813e−3 | 7.9739e−4 | 0.8895e−2 |
0.60 | 3.6642e−4 | 7.8242e−3 | 4.9945e−4 | 8.7237e−3 | 7.5491e−4 | 0.8837e−2 |
0.72 | 2.9685e−4 | 7.8239e−3 | 4.0462e−4 | 8.7235e−3 | 6.1158e−4 | 0.8837e−2 |
0.84 | 1.8851e−4 | 7.9457e−3 | 2.5655e−4 | 8.8452e−3 | 3.8769e−4 | 0.8959e−2 |
0.96 | 0.5579e−4 | 9.0292e−3 | 0.7499e−4 | 9.9277e−3 | 1.1317e−4 | 1.0041e−2 |