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 Runge-Kutta 4th order method (RK4) is a widely used technique for solving ordinary differential equations (ODEs).
It is a more accurate and efficient method compared to the 2nd order Runge-Kutta method, as it uses four estimates of the derivative at different points to calculate the next solution estimate.
Here is the code of a Python program that implements the Runge-Kutta 4th order method for a given ODE:
Runge-Kutta 4th Order Method in Python
import math
def rk4_solver(f, y0, t0, tf, h):
# Runge-Kutta 4th Order Method [By Bottom Science]
t = t0
y = y0
while t <= tf:
k1 = h * f(t, y)
k2 = h * f(t + h/2, y + k1/2)
k3 = h * f(t + h/2, y + k2/2)
k4 = h * f(t + h, y + k3)
y = y + (k1 + 2*k2 + 2*k3 + k4) / 6
t = t + h
return y
import numpy as np
def f(t, y):
return math.sin(t) - y
y0 = 0
t0 = 0
tf = 10
h = 0.1
y_sol = rk4_solver(f, y0, t0, tf, h)
print("Solution at t = ", tf, " is: ", y_sol)
# OUTPUT - Solution at t = 10 is: 0.07776903758337268
