Runge Kutta for system of differential equations

Hello,

I have to solve the following system with method of Runge Kutta:

y1' = y2

y2'=f(x,y1,y2) with y1(0)=0 and y2(0)=y20

where f(x,y1,y2) = -axy1-y1, a=0.03 and y20 = 0.25

[James Tursa]

What have you done so far? What specific problems are you having with your code? Do you have to manually code the RK method or are you allowed to use ode45?

[Melda Harlova]

Thanks for your interest.

Here is the task with corrections:

y1' = y2

y2'=f(x,y1,y2) with y1(0)=0 and y2(0)=y20

where f(x,y1,y2) = -axy2-y1, a=0.03 and y20 = 0.25

And here is my solution. What is im not sure about is x = 0 : h : 2*pi; and figure(2), plot(x, y(1,:), x, ??, ‘*’)

from code and if my code is correct at all. I have been solved similar task but without any given , a=0.03 and y20 = 0.25.

Function main

h = pi/10;

x = 0 : h : 2*pi;

n = length(x);

y(1,1)=0; y(2,1) = 0,25;

for k = 1: (n-1)

k1 = h * rung(x(k), y(1:2,k));

k2 = h * rung(x(k) + h/2; y(1:2,k) + k1/2);

k3 = h * rung(x(k) + h/2; y(1:2,k) + k2/2);

k4 = h * rung(x(k) + h; y(1:2,k) + k3);

y(1:2,k+1)=y(1:2,k) + (k1 + 2*k2 + 2*k3 + k4)/6;

end

figure(1), plot(x, y(2,:)) %everything from second row

figure(2), plot(x, y(1,:), x, ??, ‘*’)

function f=rung(x,y)

f(1,1) = y(2);

f(2,1) = -0,03*x*y(2) – y(1);

[Jan]

@Melda: Fine. Now what exactly is your question?

[Melda Harlova]

I already mentioned that im not sure about

1) x = 0 : h : 2*pi; and

2)figure(2), plot(x, y(1,:), x, ??, ‘*’).

Sooo the question is what have to be there where is the question marks and is this is correct x = 0 : h : 2*pi

or is there another way to write 2)

[Jan]

I cannot know, what you want to insert for the questionmarks in

plot(x, y(1,:), x, ??, ‘*’)

because you did not explain, what you want to achieve. x=0:h:2*pi can be correct of false depending on what you want as values for x. It is impossible to decide if something is correct or not only based on the code. Knowing its purpose is essential.

By the way, use single quotes instead of the apostrophes:

plot(x, y(1,:), x, ??, ‘*’)
%                      ^ ^  Use '

[Melda Harlova]

Oh yees, thank u for apostrophes.

In the example that i have instead of question marks is the exact solution. But here in this example i dont know the exact solution what is. Also i dont know if without exact solution will be correct.