Research Article
On Corrected Quadrature Rules and Optimal Error Bounds
Table 4
Results for the midpoint rule.
| Midpoint rule |
| | Standard rule () | Computed | Absolute error | Relative error | Estimated order | integral | ABS() | REL() | |
| 5 | 1.4527054409211020 | 0.0062641086729669 | | ā | 10 | 1.4479877945462096 | 0.0015464622980745 | | 2.0 | 15 | 1.4471270587692653 | 0.0006857265211302 | | 2.0 | 20 | 1.4468267417338132 | 0.0003854094856781 | | 2.0 | 25 | 1.4466879021519083 | 0.0002465699037733 | | 2.0 |
| | Corrected rule () | Computed | Absolute error | Relative error | Estimated order | integral | ABS() | REL() | |
| 5 | 1.4465452831301751 | 0.0001039508820400 | | ā | 10 | 1.4464477550984778 | 0.0000064228503427 | | 4.0 | 15 | 1.4464425967924956 | 0.0000012645443606 | | 4.0 | 20 | 1.4464417318718803 | 0.0000003996237452 | | 4.0 | 25 | 1.4464414958402714 | 0.0000001635921363 | | 4.0 |
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