smiley-epsilon

A library of tools for numerical methods used in engineering applications.

Repository Structure

.
├── figures
│   ├── functions
│   │   ├── f1.eps
│   │   ├── f2.eps
│   │   ├── f3.eps
│   │   ├── f4.eps
│   │   └── f5.eps
│   ├── jacobi.eps
│   ├── open-flowchart.eps
│   └── roots
│       ├── f1.eps
│       ├── f1.txt
│       ├── f2.eps
│       ├── f2.txt
│       ├── f3.eps
│       ├── f3.txt
│       ├── f4.eps
│       ├── f4.txt
│       ├── f5.eps
│       ├── f5.txt
│       └── figures
│           └── roots
├── functions
│   ├── delta1.m
│   ├── delta2.m
│   ├── delta3.m
│   ├── delta4.m
│   ├── delta5.m
│   ├── f1.m
│   ├── f2.m
│   ├── f3.m
│   ├── f4.m
│   └── f5.m
├── gauss_jordan.m
├── gauss_seidel_legacy.m
├── gauss_test.m
├── integration
│   ├── f_test.m
│   ├── integrate.m
│   ├── README.md
│   ├── report
│   │   ├── figures
│   │   │   └── uneven.eps
│   │   └── report.pdf
│   ├── simpson13.m
│   ├── simpson38.m
│   ├── test.m
│   └── trapezoidal.m
├── jacobi.m
├── jacobi_test.m
├── LICENSE
├── matrices
│   └── linear_eq.mat
├── octave
│   ├── bisect.m
│   ├── bisect_test.m
│   ├── bisect_test_script.m
│   ├── bracketing.m
│   ├── compute_ea.m
│   ├── gauss_seidel.m
│   ├── newton_raphson.m
│   └── open_method.m
├── plot_f.m
├── README.md
└── roots
    ├── bracketing.m
    ├── compute_ea.m
    ├── generic_secant.m
    ├── legacy
    │   ├── bisect.m
    │   ├── bisect_test.m
    │   └── bisect_test_script.m
    ├── newton_raphson.m
    ├── solutions
    │   ├── f1.txt
    │   └── figures
    │       └── roots
    └── solveplot.m

Scope

This readme is to describe folder structures and the nitty-gritty details of what each file can do. For an overall description, please see the reports compiled in Latex. This readme is accompanied by two technical reports for each part.

Part 1

Root finding for non-linear equations

1. Bisection Method
2. False Position Method
3. Secant Method
4. Modified Secant Method
5. Newton-Raphson Method

Solving Systems of Linear equations

1. Gauss-Jordan Elimination
2. Jacobi Iteration of Gauss-Seidel

Functions and Derivatives

We place functions and their derivatives in functions. A function for the ($i)ith test is called f$i.m and its derivative is called delta$i.m

Part 2

Folder structures

.
├── f_test.m              The test function as a blackbox [please see the report]
├── integrate.m           Numerical Integration for given uneven segments
├── simpson13.m           Simpson's 1/3 rule
├── simpson38.m           Simpson's 3/8 rule
├── test.m                A test script to test the whole script
└── trapezoidal.m         The trapezoidal rule

Implementation Notes

1. Since the goal is to eventually code an algorithm to evaluate the integral by using combinations of the rules [as written in the project requirements], we code only single application of each of them and leave the multiple application for the combining algorithm.