Plotting in python using matplotlib?

Question

I have been trying to simulate the first order differential equation using the fourth order Runge-Kutta method , but I am having problems plotting it.

#simulation of ode using 4th order rk method  dy/dx=-2y+1.3e^-x,y(0)=5,h=0.01 from sympy import*
import math
import numpy as np
import matplotlib.pyplot as plt
h=0.01;
ti=0;
x=0;
n=0;
y=5;
def f(x,y):
    return 1.3*math.exp(-x)-2*y


while x < 10:

    k1=f(x,5);
    k2=f(x+h/2,y+(h/2)* k1);
    k3=f(x+h/2,y+(h/2)* k2);
    k4=f(x+h,y+h*k3);
    y=y+h/6*(k1+2*(k2+k3)+k4);
    x=x+h;
    plt.plot(x,y);

I know that the problem is because of updating the x,y values every time the loop runs, but can somebody explain how to plot all the values of (x,y)?

Answer 1

As suggested in the comment, you can create two lists to store x and y values and plot it after the while loop:

import math
import numpy as np
import matplotlib.pyplot as plt
h=0.01;
ti=0;
x=0;
n=0;
y=5;
def f(x,y):
    return 1.3*math.exp(-x)-2*y

xs = [x]       # <<<
ys = [y]       # <<<
while x < 10:

    k1=f(x,5);
    k2=f(x+h/2,y+(h/2)* k1);
    k3=f(x+h/2,y+(h/2)* k2);
    k4=f(x+h,y+h*k3);
    y=y+h/6*(k1+2*(k2+k3)+k4);
    x=x+h;
    xs.append(x)    # <<<
    ys.append(y)    # <<<

plt.plot(xs,ys);

Answer 2

Another source for wrong results is the first line in the RK4 loop. Instead of

    k1=f(x,5);

use

    k1=f(x,y);

since the value of y does not stay constant at the initial value.