Nonlinear differential equations

Question

Zaynab 2012-4-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/34669-nonlinear-differential-equations

评论： linger 2021-10-10

Hi,

How can i solve a system of nonlinear differential equations using Matlab?? here is an example of what i'm talking about it's not the problem that i'm working in but it had the same form. //// x'=3x+y//// y'=y-x+y^4+z^4//// z'=y+z^4+y^4+3/// the ' means the derivative. i'll appreciate your help, best regards!

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Answer 1

Andrei Bobrov 2012-4-6

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https://ww2.mathworks.cn/matlabcentral/answers/34669-nonlinear-differential-equations#answer_43506

在 MATLAB Online 中打开

Pleace read about solve initial value problems for ordinary differential equations

eg for your case

f1 = @(t,y)[3*y(1)+y(2);y(2)-y(1)+y(2).^4+y(3).^4;y(2)+y(2).^4+y(3).^4+3]
[T,Y] = ode45(f1,[0 .1],zeros(3,1))

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linger 2021-10-10

how about using other methods to solve this example ? such as Euler method and Midpoint method. Could you solve it?

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Answer 2

Zaynab 2012-4-6

2
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https://ww2.mathworks.cn/matlabcentral/answers/34669-nonlinear-differential-equations#answer_43543

在 MATLAB Online 中打开

Thanks andrei bobrov,

Actually the link is verry helpful, i used the ode45 solver too and i print the system.Here is the programme

function dy = zin(t,y)
dy = zeros(3,1);    
dy(1) = 3*y(1)+y(2);
dy(2) = y(2)-y(1)+y(2).^4+y(3).^4;
dy(3) = y(2)+y(3).^4+3+y(2).^4;    
end
      options = odeset('RelTol',1e-2,'AbsTol',[1e-2 1e-2 1e-2]);
      [T,Y] = ode45(@zin,[0 12],[0 1 1],options);
      plot(T,Y(:,1),'-',T,Y(:,2),'-.',T,Y(:,3),'.');