Category: Numerical Analysis

Blog Entry © Tuesday, January 14, 2025, by James Pate Williams, Jr. Solution of an 8×8 System of Nonlinear Equations Using a Hybrid Algorithm

Hybrid System of Nonlinear Equations Solver V1Download

Blog Entry © Tuesday, January 7 – Thursday, January 9, 2025, by James Pate Williams, Jr. Solution of a System of Nonlinear Equations Using Damped Newton’s Method for a System of Equations

Damped Newton’s Method for a Nonlinear System of EquationsDownload

Blog Entry © Wednesday, January 1, 2025, by James Pate Williams, Jr Solution of a 4×4 System of Nonlinear Equations Using a Homegrown Evolutionary Hill-Climber

Blog Entry January 1 2025Download

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First United Methodist Church (FUMC) of LaGrange Georgia Historical Attendance Data for the Year of 2006 © James Pate Williams, Jr., BA, BS, Master Software Engineering, PhD and FUMC Friday, December 20, 2024, to Tuesday, December 24, 2024

FUMC Attendance Data for 2006Download

Blog Entry © Saturday, November 30, 2024, by James Pate Williams, Jr. Partial Solution of the Schrödinger Equation for Hydrogen in Parabolic Coordinates

Solution of the Schrödinger Equation for Hydrogen in Parabolic CoordinatesDownload

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 Sunday 11 17 2024Download