Plotting third order differential equation using ode45

Question

vaibhav gupta 2020-12-6

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https://ww2.mathworks.cn/matlabcentral/answers/682958-plotting-third-order-differential-equation-using-ode45

评论： Ameer Hamza 2020-12-7

采纳的回答： Ameer Hamza

Hello

Could you please how to plot below third order differential equation using ODE45.

d3x/dt3 = +-1

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Answer 1

Ameer Hamza 2020-12-6

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https://ww2.mathworks.cn/matlabcentral/answers/682958-plotting-third-order-differential-equation-using-ode45#answer_567083

编辑：Ameer Hamza 2020-12-6

在 MATLAB Online 中打开

You need to convert this 3-rd order ODE to 3 first order ODEs. Also due to +-1, you have two systems of ODEs. Try following code

odeFun = @(t,x,a) [x(2);
                   x(3);
                   a];
tspan = [0 10];
IC = [1; 0; 0];
ode45(@(t,x) odeFun(t,x,1), tspan, IC)
hold on
ode45(@(t,x) odeFun(t,x,-1), tspan, IC)
legend({'$x$', '$\dot{x}$', '$\ddot{x}$'}, 'Interpreter', 'latex', 'FontSize', 16, ...
    'Location', 'best')

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vaibhav gupta 2020-12-6

编辑：vaibhav gupta 2020-12-6

Thank you! I just wanted to plot result of first ode. How can i supress rest? Also, i see that plot is continuing and not stopping at all. Shoudln't it be stopped rendering at some point of time?

Ameer Hamza 2020-12-7

在 MATLAB Online 中打开

Try this

odeFun = @(t,x,a) [x(2);
                   x(3);
                   a];
tspan = [0 10];
IC = [1; 0; 0];
[t, y] = ode45(@(t,x) odeFun(t,x,1), tspan, IC);
plot(t, y(:,1))
hold on
[t, y] = ode45(@(t,x) odeFun(t,x,-1), tspan, IC);
plot(t, y(:,1))
legend({'$+1$', '$-1$'}, ...
    'Interpreter', 'latex', ...
    'FontSize', 16, ...
    'Location', 'best')