how to solve non linear differential equations

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))

Answer 1

[Bjorn Gustavsson]

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

[nune pratyusha]

it showing error like

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched

delimiters.

please refer any supplimentary materials for solving non linear differential equation in matlab

[Bjorn Gustavsson]

OK, now edited/corrected the code.

[nune pratyusha]

edited code also showing error

[Bjorn Gustavsson]

Now edited and tested.

[nune pratyusha]

It's not working

[Walter Roberson]

Nope, it is working.

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);

plot(t,xy)

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];
end

[nune pratyusha]

but in my system it showing error

[nune pratyusha]

error

[Bjorn Gustavsson]

Have you included all the corrections to your_ode.m?

[nune pratyusha]

yes

[nune pratyusha]

now its working thank you sir, but i want output as sin wave

[nune pratyusha]

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]

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.