https://github.com/brayvid/numerical-analysis
Algorithms from "Numerical Analysis" by Burden and Faires.
https://github.com/brayvid/numerical-analysis
differential-equations interpolation linear-algebra numerical-methods root-finding
Last synced: 11 months ago
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Algorithms from "Numerical Analysis" by Burden and Faires.
- Host: GitHub
- URL: https://github.com/brayvid/numerical-analysis
- Owner: brayvid
- Created: 2018-12-13T13:42:19.000Z (about 7 years ago)
- Default Branch: master
- Last Pushed: 2018-12-17T01:20:07.000Z (about 7 years ago)
- Last Synced: 2025-01-11T11:18:27.255Z (about 1 year ago)
- Topics: differential-equations, interpolation, linear-algebra, numerical-methods, root-finding
- Language: MATLAB
- Homepage:
- Size: 12.7 KB
- Stars: 0
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Numerical Analysis Algorithms
Matlab scripts and functions developed from theory presented in [Numerical Analysis 9e](https://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/0538733519 "Numerical Analysis 9e at Amazon.com") by Burden, Faires.
```matlab
>> Examples
```
```console
Bisection method
ans =
10×2 table
n p_n
__ ______
1 1.5
2 1.25
3 1.125
4 1.1875
5 1.1562
6 1.1406
7 1.1484
8 1.1445
9 1.1465
10 1.1455
Fixed-point iteration
ans =
5×2 table
n pn
_ _______
1 0.532
2 0.57528
3 0.5952
4 0.60543
5 0.61096
Newton's method
ans =
5×2 table
n p_n
_ ______
0 1
1 1.2241
2 1.1943
3 1.1937
4 1.1937
Lagrange interpolation
ans =
0.0283165*x^3 - 0.31374*x^2 + 1.43615*x - 1.15073
Natural cubic spline interpolation
ans =
7.81781*x^3 + 9.38137*x^2 + 5.35154*x + 1.11375
- 7.81781*x^3 + 3.47526*x + 0.98867
Neville's interpolation
ans =
- 2.7*x^2 + 0.21*x + 0.85
Jacobi Iteration:
ans =
1.0000
2.0000
-1.0000
1.0000
Euler's Method
ans =
4×3 table
t y dydt
____ ______ ______
1 4 5
1.15 4.75 5
1.3 5.5196 5.1304
1.45 6.3064 5.2458
Runge-Kutta 4th order
ans =
11×3 table
t y dydt
____ ______ ______
1 2 2
1.04 2.0817 2.0851
1.08 2.167 2.1815
1.12 2.2564 2.2913
1.16 2.3505 2.4172
1.2 2.45 2.5625
1.24 2.5558 2.7313
1.28 2.6689 2.929
1.32 2.7906 3.1626
1.36 2.9225 3.4414
1.4 3.0667 3.7778
```