how to solve non linear differential equations

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nune pratyusha 2021-3-3

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https://ww2.mathworks.cn/matlabcentral/answers/761201-how-to-solve-non-linear-differential-equations

评论： Bjorn Gustavsson 2021-3-5

dx(t)/dt=y(t)
dy(t)/dt=-(1/r+g+a+b|x(t)|)y(t)/c-x(t)/(lc)
t=-0.05:0.01:0.05
r = 1430; 
    a = -0.0683; 
    b = 0.0676;
    c = 36*10^-9;
    g = -0.0676;
    l=27

i want to plot phase portrait of (x(t),y(t)) and plots for (t,x(t)),(t,y(t))

回答（1 个）

Bjorn Gustavsson 2021-3-3

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/761201-how-to-solve-non-linear-differential-equations#answer_637971

编辑：Bjorn Gustavsson 2021-3-4

在 MATLAB Online 中打开

Have a look at the help and documentation of ode45 and the numerous ode-examples.

In brief to solve this ODE-system write a matlab-function for the derivatives:

function dxdtdydt = your_ode(t,xy,pars)
r = pars(1);
a = pars(2);
b = pars(3);
c = pars(4);
g = pars(5);
l = pars(6);
y = xy(2);
x = xy(1);
dxdt = xy(2);
dydt = -(1/r+g+a+b*abs(x)*y/c-x/(l*c));
dxdtdydt = [dxdt;
            dydt];

That ode you then integrate from some initial state over some time-period of interest

r = 1430; 
a = -0.0683; 
b = 0.0676;
c = 36*10^-9;
g = -0.0676;
l=27;
pars = [r,a,b,c,g,l];
t = -0.05:0.01:0.05;
x0y0 = [0,1]; % I wouldn't know.
[t,xy] = ode45(@(t,xy) your_ode(t,xy,pars),t,x0y0);

HTH

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nune pratyusha 2021-3-5

dx(t)/dt=y(t)

dy(t)/dt=-(1/r+g+a+b|x(t)|)y(t)/c-x(t)/(lc)

t=-0.05:0.01:0.05

r = 1430;

a = -0.0683;

b = 0.0676;

c = 36*10^-9;

g = -0.0676;

l=27

i want to plot(t,x(t)) and plot(t,y(t))

Bjorn Gustavsson 2021-3-5

Well the solution does not look like a sine-wave. That is because I have yet another typo in the ODE, you will surely find it if you look close and read the code, and think about what you need to obtain an oscillating solution.

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