Theory and Modern Applications
Methods | λ | Time steps |  | x  = 0.1 | x  = 0.2 | x  = 0.3 | x  = 0.4 | x  = 0.5 |
---|---|---|---|---|---|---|---|---|
Proposed \(O(k^{2}+h^{4})\)- | 0.5 | 16 | u | 2.09 (−11) | 2.63 (−11) | 1.23 (−10) | 1.93 (−10) | 2.85 (−10) |
\(u_{xx}\) | 5.06 (−09) | 1.54 (−08) | 6.00 (−08) | 3.40 (−08) | 3.87 (−08) | |||
\(O(k^{2}+h^{4})\)-method in [33] | 0.5 | 16 | u | 7.46 (−10) | 2.91 (−10) | 8.65 (−10) | 6.87 (−10) | 6.98 (−10) |
\(O(k^{4}+h^{4})\)-method in [33] | 0.5 | 16 | u | 6.25 (−10) | 2.22 (−10) | 4.53 (−10) | 4.41 (−10) | 5.03 (−10) |