Help me with coupled ode45 equations in matlab

In summary, the problem is to convert a system of coupled differential equations into code using MATLAB's ode45 solver. The equations involve changing positions and various parameters, and the goal is to plot the solution for the given time span.
  • #1
sophieji
1
0
Help me with coupled ode45 equations in MATLAB please

I have no idea to turn these into MATLAB code, and here is the porblem:
y(1)' = y(2)
y(2)' = - (r+re)/(L+le)*y(2) - y(1)/c*(l+le)
y(3)' = y(4)
y(4)' = -c*y(4).^2 /m+L*y(2).^2/(2*m)
where
re = ro+Rpr*z+Lpr*z'
le = Lo+Lpr*z
the rest parameters are given numbers, and z is the changing position, the variable.
the given task is like this, two differential equations:
(L+le)*q''+(r+re)*q'+q/c=0
z''+c*(z')^2/m=Lpr*(q').^2/(2*m)
I appreciate your help!
 
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  • #2
Here is one solution using the ode45 solver in MATLAB:% Define constants r = 0.2;L = 0.3;c = 0.5;m = 1;Rpr = 0.4;Lpr = 0.6;Lo = 0.1;ro = 0.05;% Define system of equationsdydt = @(t,y) [y(2); -(r+ro+Rpr*y(1)+Lpr*y(3))/(L+Lo+Lpr*y(1))*y(2) - y(1)/c*(L+Lo+Lpr*y(1)); y(4); -c*y(4).^2/m + Lpr*y(2).^2/(2*m)];% Set initial conditionsy0 = [0; 0; 0; 0];% Choose time steptspan = [0 10];% Solve the system [t,y] = ode45(dydt, tspan, y0);% Plot the solution plot(t,y)xlabel('time')ylabel('y')legend('y1','y2','y3','y4')
 

1. How do I set up coupled ODE equations in MATLAB?

In order to set up coupled ODE equations in MATLAB, you will need to define your equations using anonymous functions or MATLAB function files. These equations should be in the form of dy/dt = f(t,y), where y is a vector of your dependent variables. Then, you can use the ode45 function to solve the equations.

2. What is the syntax for using ode45 in MATLAB?

The syntax for using ode45 in MATLAB is [t,y] = ode45(@odefun,tspan,y0), where @odefun is the function handle for your ODE equations, tspan is the time span for the simulation, and y0 is the initial condition for your dependent variables.

3. How can I visualize the results of my coupled ODE equations in MATLAB?

To visualize the results of your coupled ODE equations in MATLAB, you can use the plot function to plot your dependent variables as a function of time. You can also use other functions such as subplot to plot multiple variables on the same graph, or surf to create a surface plot.

4. Can I solve a system of higher order ODEs using ode45 in MATLAB?

Yes, you can use ode45 to solve a system of higher order ODEs in MATLAB. To do this, you will need to convert your higher order ODEs into a system of first order ODEs by defining new variables for the higher order derivatives.

5. How can I improve the accuracy of my ode45 simulations in MATLAB?

To improve the accuracy of your ode45 simulations in MATLAB, you can adjust the error tolerances using the odeset function. You can also decrease the time step size or use a different solver, such as ode23 or ode113, which may be more suitable for your particular system of equations.

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