Category: C++ Computer Applications

Blog Entry Sunday, June 16, 2024 (c) James Pate Williams, Jr. Chapter 4 Matrices and Systems of Linear Equations from a Textbook by S. D. Conte and Carl de Boor

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Blog Entry Friday, June 14, 2024 (c) James Pate Williams, Jr.

For the last week or so I have been working my way through Chapter 3 The Solution of Nonlinear Equations found in the textbook “Numerical Analysis: An Algorithmic Approach” by S. D. Conte and Carl de Boor. I also used some C source code from “A Numerical Library in C for Scientists and Engineers” by H. T. Lau, PhD. I implemented twenty examples and exercises from the previously mentioned chapter.

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Blog Entry June 5-7, 2024, (c) James Pate Williams, Jr. All Applicable Rights Reserved Chapter 7 Example and Some Exercises from “Numerical Analysis: An Algorithmic Approach (c) 1980 by S. D. Conte and Carl de Boor (Numerical Differentiation and Numerical Integration)

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Blog Entry for Early Morning Friday, May 31, 2024, Solutions of a Second Order Self-Adjoint Ordinary Differential Equation by Three Methods

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Text and Exercise from “Boundary Value Problems Second Edition” by David L. Powers in Progress (c) Wednesday, April 17, 2024, James Pate Williams, Jr.

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Solution of the One-Dimensional Heat Equation for a Rod Using Finite Differences by James Pate Williams, Jr. Created on Wednesday April 3, 2024

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Undamped Mass-Spring Eigenvalue – Eigenvector Problem by James Pate Williams, Jr. (c) Monday April 1, 2024

We extend the results of the following website:

https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/3%3A_Systems_of_ODEs/3.6%3A_Second_order_systems_and_applications

The five masses in the problem have a maximum value of 8. The six springs have a maximum value of 4 for their Hooke’s coefficients. The first 5 by 5 matrix is the inverse mass matrix, the second matrix is the Hooke’s coefficient 5 by 5 matrix, the third 5 by 5 matrix is the product of the inverse mass matrix times the Hooke’s coefficient matrix. The final row vector is the eigenvalue vector.