The Runge-Kutta method | |||||||
Step size | 4th order | 6th order | 7th order | ||||
Error | Time in Second | Error | Time in Second | error | Time in Second | ||
dt/1 = 0.01 | Inf | 1.4 | Inf | 6.2 | Inf | 3.9 | |
Dt/2 = 0.005 | 2216.9968 | 1.4 | Inf | 6.0 | Inf | 4.2 | |
Dt/4 = 0.0025 | 174.5643 | 1.4 | 320,083.898274 | 6.0 | 319,518.685882 | 3.8 | |
Dt/8 = 0.00125 | 12.2611 | 1.4 | 2,539,526.94512 | 6.0 | 2,539,945.04633 | 3.8 | |
dt/16 = 0.000625 | 0.8125 | 1.4 | 1,186,189.72471 | 6.0 | 1,189,148.66528 | 3.9 | |
Dt/32 = 0.0003125 | 0.0523 | 1.4 | 273,214.706571 | 6.0 | 272,023.301318 | 3.7 | |
Dt/64 = 0.00015625 | 0.0033 | 2.1 | 217,761.337783 | 6.0 | 216,946.587361 | 3.9 | |
Dt/128 = 7.8125e−5 | 4.6614e−5 | 1.4 | 3204.148445892 | 6.0 | 3139.59110565 | 3.9 | |
Dt/256 = 3.90625e−5 | ERROR LIMIT SATISFIED | 55.9530969299 | 6.0 | 55.7923759269 | 3.8 | ||
Dt/512 = 1.953125e5 |
| 2.735944731744 | 6.0 | 2.72836970305 | 3.8 | ||
Dt/1024 = 9.765625e−6 |
| ERROR LIMIT SATISFIED | ERROR LIMIT SATISFIED | ||||
Total Time to execution | 12.0 | 66.2 | 42.5 |