Boris - 1 year ago 107

Python 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)?

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Answer Source

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);
```

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