Bottom SciencePython Programming
Basics
Numerical Methods
- Bisection Method
- Secant Method
- Regular Falsi (False Position) Method
- Newton Raphson Method
- Gauss Elimination Method
- Gauss Jordan Method
- Gauss-Seidel Method
- Lagrange Interpolation Method
- Newton Divided Difference Interpolation
- Newton Forward Difference Interpolation
- Newton Backward Difference Interpolation
- Trapezoidal Rule
- Simpson 1/3rd Rule
- Simpson 3/8 Rule
- Euler’s Method
- Euler’s Modified Method
- Runge-Kutta 2nd Order Method
- Runge-Kutta 4th Order Method
- Cubic Spline Method
- Bilinear Interpolation Method
- Milne’s Method
- More topics coming soon…
Advance Numerical Methods
The Simpson’s 3/8 rule is a numerical integration method that approximates the definite integral of a function between two limits.
It states that given a function f(x) defined on the interval [a,b], the definite integral of f(x) from a to b can be approximated by:
integral of f(x) from a to b is approximately
(b – a) * [f(a) + 3f(a + (b-a)/3) + 3f(a + 2*(b-a)/3) + f(b)]/8
Simpson 3/8 Rule in Python
def simpsons_3_8_rule(f, a, b, n):
# Simpson 3/8 Rule [By Bottom Science]
h = (b - a) / n
s = f(a) + f(b)
for i in range(1, n, 3):
s += 3 * f(a + i * h)
for i in range(3, n-1, 3):
s += 3 * f(a + i * h)
for i in range(2, n-2, 3):
s += 2 * f(a + i * h)
return s * 3 * h / 8
def f(x):
return x**2
a = 0
b = 1
n = 100
result = simpsons_3_8_rule(f, a, b, n)
print(result)
#OUTPUT - 0.3138
