Category: Computer Science
Blog Entry (c) Thursday, November 21, 2024, by James Pate Williams, Jr. Comparison of Homegrown Fifth Order Runge-Kutta Method Versus a Limited Number of Predictor-Corrector Algorithm
The first table is based on Conte-de Boor Fourth Runge-Kutta formulas that I converted to Fifth Order Runge-Kutta. Initial values: V = 2600 feet per second angle of elevation 30 degrees diameter 16 inches coefficient of form 0.61 density ratio 1.00 are from LCDR Ernest Edward Herrmann’s Exterior ballistics, 1935 My results are given first then LCDR Herrmann’s results:
| x | deg | min | sec | time | v | vx | vy | y |
|---|---|---|---|---|---|---|---|---|
| 0 | 30 | 0 | 0 | 0.00 | 2600 | 2252 | 1300 | 0 |
| 563 | 29 | 50 | 45 | 0.25 | 2578 | 2236 | 1283 | 325 |
| 1122 | 29 | 41 | 24 | 0.50 | 2556 | 2221 | 1266 | 646 |
| 1677 | 29 | 31 | 57 | 0.75 | 2535 | 2206 | 1250 | 962 |
| 2229 | 29 | 22 | 25 | 1.00 | 2515 | 2191 | 1233 | 1275 |
| 2776 | 29 | 12 | 47 | 1.25 | 2494 | 2177 | 1217 | 1583 |
| 3321 | 29 | 3 | 4 | 1.50 | 2474 | 2163 | 1201 | 1887 |
| 3861 | 28 | 53 | 15 | 1.75 | 2455 | 2149 | 1186 | 2188 |
| x | deg | min | sec | time | v | vx | vy | y |
|---|---|---|---|---|---|---|---|---|
| 0 | 30 | 0 | 0 | 0.00 | 2600 | 2252 | 1300 | 0 |
| 561 | 29 | 50 | 7 | 0.25 | 2582 | 2259 | 1285 | 323 |
| 1120 | 29 | 41 | 4 | 0.50 | 2564 | 2227 | 1270 | 642 |
| 1675 | 29 | 32 | 2 | 0.75 | 2546 | 2216 | 1255 | 958 |
| 2228 | 29 | 22 | 5 | 1.00 | 2529 | 2204 | 1241 | 1270 |
It is amazing how accurate Herrmann’s results were based on only a couple iterations using the Mayevski seven zone velocity retardation formulas.
Blog Entry © Sunday, November 17, 2024, by James Pate Williams, Jr. Three Methods of Solving the Exterior Ballistics Problem for the Fast Battleship USS Iowa (BB-61) 16-Inch/50 Caliber Rifles
Blog Entry © Saturday, November 16, 2024, by James Pate Williams, Jr., The Microsoft Copilot
Blog Entry © Thursday, November 14, 2024, by James Pate Williams, Jr.
Blog Entry © Wednesday, November 6, 2024, by James Pate Williams, Jr. Particle in a Finite Spherical Three-Dimensional Potential Well
The Bessel functions are from A Numerical Library in C for Scientists and Engineers (c) 1995 by H. T. Lau, PhD.
Blog Entry © Friday, November 1, 2024, by James Pate Williams, Jr. Calculation of the Overlap Matrix for the Water Molecule (H2O) Using a Contracted Set of Gaussian Orbitals
Reference: https://content.wolfram.com/sites/19/2012/02/Ho.pdf
I reproduced most of the computations in the MATHMATICA reference. The water molecule is a planar molecule that lies in the YZ-plane.
