diffeq.py

Created on June 09, 2023
774 Bytes
# DE Numerical Methods
from math import *

#define the function
def f(t,y): return (cos(t)-y)/(t+1)

def run():
    print("1:Euler    2:RK4")
    type=int(input("?"))
    x0 = float(input("x0="))
    y0 = float(input("y0="))
    h  = float(input("h="))
    N = int(input("N="))      
    if type == 1: euler(f,x0,y0,h,N)
    if type == 2: RK(f,x0,y0,h,N)
            
def euler(f,x0,y0,h,N):
  for i in range(1,N+1):
    y0 += h*f(x0,y0)
    x0 += h
    print(round(x0,5),"  ",round(y0,5))
  

# Runge-Kutta
# RK(f,x0,y0,h,N)
def RK(f,x0,y0,h,N):
  for i in range(1,N+1):
    k1 = f(x0,y0)
    k2 = f(x0+.5*h,y0+.5*h*k1)
    k3 = f(x0+.5*h,y0+.5*h*k2)
    k4 = f(x0+h,y0+h*k3)
    y0 += h*(k1+2*k2+2*k3+k4)/6
    x0 += h
    print(round(x0,5),"  ",round(y0,9))