solving nonlinear diffrential equation using ode45
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I have never met this kind of non-linear equation, and this is my current code
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function homework1 = main1(t,X)
global m c k1 k3
A = [ -c/m -k1/m; 1 0 ] ;
f = 0.*((t>=0)-(t>=10))+ (3*cos(t^2)).*((t>10)-(t>=30))+(-10).*((t>30)-(t>=50));
F=[f/m;0];
C=X*[0 0;1 0] ;
B=C.^3;
homework1= [X(2);A*X-k3/m*B+F] ;
-------
clear all
close all
global m c k1 k3
m = 1; c = 0.02 ; k1 = 1.25; k3=0.05;
tspan= 0:0.1: 50 ;
X0 = [ -3, 5 ] ;
[ t X ] = ode45(@main1, tspan, X0);
-------
what I am specially struggling with is the
- 'x^3' term, I can't express the appropriate term
- plotting (x,t) as the 't' goes on
- using ode45 is required
please help me...
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Accepted Answer
Ameer Hamza
on 19 Mar 2020
Edited: Ameer Hamza
on 19 Mar 2020
First, no need to use global variables. Using them is not a recommended practice. Second, just write your ODE inside the main1.
Write this in a script file
tspan= 0:0.1:50 ;
X0 = [5, -3] ;
[t, X] = ode45(@main1, tspan, X0);
plot(t,X)
And save the following function in the file "main1.m"
function homework1 = main1(t,X)
m = 1;
c = 0.02;
k1 = 1.25;
k3=0.05;
if t < 10
F = 0;
elseif t < 30
F = 3*cos(t.^2);
else
F = -10;
end
homework1= [X(2); -c/m*X(2)-k1/m*X(1)-k3/m*X(1).^3+F/m] ;
end
7 Comments
Ameer Hamza
on 19 Mar 2020
alsgud, for your second file, the differential equation will be different. You first have to find the differential equation and then apply the code.
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