Hi Rahiti,
I understand that you need help in solving nonlinear system of differential equations using 'ode45'. To use 'ode45' the governing equations should be of the form X' = F(X,t), where X and F are vectors. Your system of equations can be recast into this form as follows:
- Let x1 = x and x2 = y
- x1' = wLsin(x2)
- x2' = x3
- x3' = x4
- x4' = (bx1x3-wcos(x2))/a
Define these derivatives in a separate function file (func.m) and pass its handle as an argument to ode45.
function dxdt=func(t,x)
a=1;
b=0.2;
w=1;
L=0.1;
dx1dt=w*L*sin(x(2));
dx2dt=x(3);
dx3dt=x(4);
dx4dt=(b*x(1)*x(3)-w*cos(x(2)))/a;
dxdt=[dx1dt;dx2dt;dx3dt;dx4dt];
end
A sample execution is shown below
tspan = [0 5] % time interval in which equations are solved
X0 = [1 1 0 0] % initial values of x1, x2 , x3 and x4 (or x, y, y', y'')
[t,X]=ode45(@func,tspan, X0)
Refer to the documentation https://www.mathworks.com/help/releases/R2018a/matlab/ref/ode45.html for more details.
