Lab 2: Solution of Non-linear Equations using Newton-Raphson Method

from math import *
import matplotlib.pyplot as plt

f = lambda x: sin(x) * 5 - 6 * cos(x)
d = lambda x: 5 * cos(x) + 6 * sin(x)

def newton(f, d, a, tol=5e-9, max_itr=50):
  
    count = 0
    while count < max_itr:
        if abs(d(a)) <= tol:
            print("Derivative near zero. No solution found.")
            return None
        b = a - f(a) / d(a)  
        if abs(b - a) < tol:  
            return b
        a = b
        count += 1
    print("Maximum iterations reached. No solution found.")
    return None

try:
    a = float(input("Enter the initial guess (a): "))
except ValueError:
    print("Invalid input. Please enter a number.")
    exit()

solution = newton(f, d, a)

if solution is not None:
    print("The solution is:", round(solution, 6))
else:
    print("No solution found.")

X = [i * 0.1 for i in range(-100, 101)]
Y = [f(x) for x in X]

plt.plot(X,Y, label="f(x) = 5sin(x) - 6cos(x)")
plt.axhline(0, color="black", linewidth=0.5, linestyle="--")
plt.axvline(solution, color="red", linestyle="--", label=f"Root: {round(solution, 6)}" if solution else "No Root")
plt.title("Visualization of the Function")
plt.xlabel("x")
plt.ylabel("f(x)")
plt.legend()
plt.grid(True)
plt.show()