PS3: ODE Numerical Methods
8.2: Comparison of Euler and Runge-Kutta Methods
| Method | Step Size | Average Error | Final Error | Final Slope |
|---|
| Euler | 1.0 | 0.818325 | 0.987344 | -1.0 |
| 0.1 | 0.022070 | 0.002772 | -0.071785 |
| 0.01 | 0.002766 | 2.8511×10-5 | 0.007956 |
| 0.001 | 3.1414×10-4 | 1.2275×10-7 | 2.5227×10-4 |
| Runge-Kutta | 1.0 | 0.456311 | 1.036285 | 0.138248 |
| 0.1 | 8.3365×10-5 | 3.7229×10-5 | 0.059490 |
| 0.01 | 8.3142×10-9 | 4.5941×10-10 | 0.009265 |
| 0.001 | 2.0247×10-10 | 1.1968×10-13 | 2.6536×10-4 |
8.3: Adaptive Stepper Runge-Kutta
| Initial Step Size | Error Tolerance | Average Step Size | Average Error | Final Error | Final Slope |
|---|
| 0.1 | 1 | 1.712500 | 0.848696 | 0.705358 | 0.350643 |
| 0.1 | 1.703243 | 0.604294 | 0.714263 | -0.055028 |
| 0.01 | 0.835904 | 0.312087 | 0.944032 | 0.096825 |
| 0.001 | 0.475492 | 0.180770 | 0.221747 | 0.213692 |
| 0.0001 | 0.399365 | 0.083443 | 0.012006 | 0.021980 |
| 0.00001 | 0.211074 | 0.069431 | 0.028222 | -0.227655 |