Solve 2nd order ODE using Euler Method

VERY new to Matlab...

Trying to implement code to use Euler method for solving second order ODE.

Equation:

x'' + 2*z*w*x' + w*x = 2*sin(2*pi*2*t)

z and w are constants. "t" is time.

Any help would be great.

Thanks!

[John D'Errico]

If you need to solve that ODE, then why in the name of god are you writing an Euler's method to solve the ODE. Use ODE45. Do not write your own code. Since the only reason you need to use Euler's method is to do this as a homework assignment, then you need to write your own code. But Answers is not a service where we do your homework with no effort shown by you.

[Matt]

This is a HW assignment. No need to be a jerk about it. If you don't want to help then don't post.

[Matt]

So, I've been going at it a different way but still getting errors...

%Euler solution for ODE function

HW2_Parameters % Load initial conditions into the workspace

t0 = 0 ;

n1 = (tn-t0)/h ;

for i=1:n1

t(i+1) = t0 + i*h ;

x_dd(i) = (2*sin(2*pi*2*t(i))) - (2*zeta*omega_n*x_d(i-1)) - (omega_n*x(i-1));

x_d(i) = x_d(i-1) + (x_dd(i)*h);

x(i) = x(i-1) + (x_d(i)*h);

end

Any thoughts?

[James Tursa]

@Matt - FYI, when you get errors, it is best to post the entire error message along with your code. Regardless, see my answer below ...

[Matt]

Will do. Really new here so just learning the ways about this. I'll be back! :-)

Answer 1

[James Tursa]

You start your loop with i=1, but that means your x_d(i-1) will be x_d(0), an invalid index, hence the error. You need to set initial values for x_d(1) and x(1), and then have your starting loop index be 2. E.g.,

x(1) = initial x value
x_d(1) = initial xdot value
for i=2:n1 % start loop index at 2
    x_dd(i-1) = use (i-1) indexes on everything on rhs
    x_d(i) = use (i-1) indexes on everything on rhs
    x(i) = use (i-1) indexes on everything on rhs

[Matt]

Worked like a charm! Thank you.

Answer 2

[Davide Masiello]

Hi Matt - a second order ODE can be decomposed into two first order ODEs.

The secret is to set 2 variables y as

The you have

An example code is

clear,clc

tspan   = [0,1];                        % integrates between times 0 and 1
x0      = [1 0];                        % initial conditions for x and dx/dt

[t,X]   = ode15s(@odeFun,tspan,x0);     % passes functions to ODE solver

x       = X(:,1);
dxdt    = X(:,2);

plot(t,x)

function dydt = odeFun(t,y)
z = 1;
w = 1;
dydt(1,1) = y(2);
dydt(2,1) = 2*z*w*y(2)-w*y(1)+2*sin(2*pi*2*t);
end

[Davide Masiello]

For more info, I suggest reading the documentation at the following link.

https://ch.mathworks.com/help/matlab/ordinary-differential-equations.html