Category: Numerical Analysis

Blog Entry © Monday, October 14, 2024, Real Eigenvalues and Eigenvectors of a 4 x 4 Tridiagonal Matrix and Solutions of a 4 x 4 System Using the Same Tridiagonal Matrix by James Pate Williams, Jr.

Two methods of solving linear systems of equations are explored in this blog. The methods are the Gauss-Seidel method and the Jacobi iteration.

Blog Entry Monday October 14 2024Download

Blog Entry © Monday, October 7, 2024, by James Pate Williams, Jr. Recent Voyages into the World of Quantum Chemistry

Blog Entry Monday October 7 2024 Some Recent Quantum ChemistryDownload

Blog Entry © Saturday, October 5, 2024, by James Pate Williams, Jr. Multidimensional Integrals

nQuadrature IntegrandsDownload

Blog Entry © Thursday, October 3, 2024, by James Pate Williams, Jr. A Mixture of Numerical Analysis and General Relativity Physics

Test Particle and Photon Traversal about the Schwarzschild SingularityDownload

Blog Entry (c) Wednesday, October 2, 2024, by James Pate Williams, Jr. First Order Coupled Ordinary Differential Equations

First Order Coupled ODEDownload

Blog Entry (c) Saturday, September 28, 2024, by James Pate Williams, Jr. New Iowa Ballistics Table

I created the following fast battleship Iowa class ballistics table using a single coefficient of form with the value 0.531. The ballistic coefficient is 19.86229.

For comparison use the actual October 1941 Iowa class ballistics tables:

https://eugeneleeslover.com/USN-GUNS-AND-RANGE-TABLES/OP-770-1.html

Click to access op-770-range-tables-for-16inch-50-caliber-gun-1.pdf

Iowa Range Table 531Download

Blog Entry © Thursday September 26, 2024, by James Pate Williams, Jr. Atmospheric Air Density Two Models

I wrote a C# program to graph NASA’s Earth Atmospheric Model’s variation of air density with height in Imperial Units and the United States Navy’s air density altitude equation.

Earth Atmosphere Model – Imperial Units (nasa.gov)

The USN’s formula for density – altitude is found in “Exterior ballistics, 1935” by Lieutenant Commander Ernest Edward Herrmann who was an instructor at the United States Naval Academy.