Theory and Modern Applications
Table 3 The Maximum absolute relative errors for Example 3 at \(\pmb{t=0.01}\) for various values of λ (uniform mesh)
λ |  | Proposed \(\boldsymbol {O(k^{2}+ h^{4})}\) -method ( 28a )-( 28b ) | \(\boldsymbol {O(k^{2}+ h^{4})}\) -method discussed in [ 33 ] | \(\boldsymbol {O(k^{4}+ h^{4})}\) -method discussed in [ 33 ] | Method discussed in [ 29 ] | Method discussed in [ 28 ] |
|---|---|---|---|---|---|---|
0.05 | u | 6.0176 (−12) | 5.21 (−08) | 5.33 (−08) | 9.90 (−08) | 1.90 (−06) |
\(u_{xx}\) | 2.4614 (−12) | |||||
0.1 | u | 4.4223 (−12) | 1.03 (−07) | 9.97 (−08) | 8.10 (−08) | 7.20 (−07) |
\(u_{xx}\) | 3.1911 (−12) | |||||
0.25 | u | 5.2459 (−12) | 3.74 (−08) | 3.51 (−08) | 6.90 (−08) | 4.10 (−07) |
\(u_{xx}\) | 4.9774 (−12) |