Theory and Modern Applications
Table 5 The absolute error ratios at some grid points on \(t=1\) and the orders \(p_{1}\), \(p_{2}\) for Example 3
From: Implicit methods for the first derivative of the solution to heat equation
x | \(r_{1}\) | \(p_{1}\) | \(r_{2}\) | \(p_{2}\) |
|---|---|---|---|---|
0.125 | 3.9544688 | 1.9835 | 3.9798658 | 1.9927 |
0.25 | 3.9607102 | 1.9858 | 3.9774606 | 1.9919 |
0.375 | 3.9675005 | 1.9882 | 3.9838160 | 1.9942 |
0.5 | 3.9777172 | 1.9917 | 3.9902057 | 1.9965 |
0.625 | 3.9893770 | 1.9962 | 3.9988519 | 1.9996 |
0.75 | 4.0086237 | 2.0031 | 4.0096819 | 2.0035 |
0.875 | 4.0379310 | 2.0136 | 4.0207972 | 2.0075 |