Category: Numerical Analysis

Blog Entry (c) Monday September 16, 2024, by James Pate Williams, Jr. Variation of the Gravitational Acceleration on Earth with Height

Variation of the Gravitational Acceleration with HeightDownload

Blog Entry (c) Saturday August 31, 2024, by James Pate Williams, Jr. An Elementary School Problem Found Online

Solve for a real root of the equation
f(x)=log6l(5+x)+log6l(x)=0
First we test our log6l(x) function
log6l(12) = 1.386853
log6l(36) = 2.000000
x = 0.1925824036
f = 0.0000000000
Online Logarithm Problem C Source CodeDownload

Blog Entry (c) Friday August 30, 2024, by James Pate Williams, Jr. Another Simple Math Problem

We use an evolutionary hill-climber and the solution of the quadratic equation to solve the easy problem below:

Solution of f(a,x)=sin(sqrt(ax-x^2))=0
Subject to the constraint x+y=100
Where x and y are the two roots of
g(a,x)=ax-x^2-n*n*pi*pi=0
and n=15
a = 100.347888933988
x = 32.947113268776
y = 67.400775665213
g =  0.000000000000
s = 100.347888933988
runtime in seconds = 43.730000
Other Online Math Problems C Source CodeDownload

Blog Entry (c) Tuesday, August 27, 2024, Two More Online Mathematics Problems by James Pate Williams, Jr.

Solution of f(t) = cos(2t) + cos(3t)
t    =  0.628318530718
f(t) =  1.11022302e-16
Solution of f(x) = sqrt(1 + sqrt(1 + x)) - x^1/3
x    =  8.000000000000
f(x) =  0.00000000e+00
Solution of f(x) = 9^x + 12^x - 16^x
x    =  -16.387968065352
f(x) =    2.32137533e-16
Solution of f(x) = 8^x-2^x - 2(6^x-3^x)
x    =  1.000000000000
f(x) =  0.00000000e+00
Other Online Mathematics Problems C Source CodeDownload

Blog Entry August 9, 2024, (c) James Pate Williams, Jr. Another Online Math Problem

The problem is to find the real root of the equation: f(x)=x^(x^8)-8=0. I use the Newton-Raphson method, a root finding algorithm. A first guess is x = 2. The solution is: x = 1.2968395547, f(x) = -2.6645353e-15. I compute the necessary derivative using central-finite differences with a step size of h = 2/10000.

Another Math Problem Source CodeDownload