How to solve and plot system of nonlinear differential equations?
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Hello,
I am having troubles solving a system of second order nonlinear equations with boundary conditions.
The equations are:
u0=4*pi*10e-7;
R=0.8;
V=10;
d=0.015;
xp1=0.002;
xp2=d-xp1;
p2=1000000;
p1=1000000;
r=0.01;
W=0.02;
g=0.001;
N=200;
x0=0.025;
k=300;
M=0.3;
B=40;
syms t x(t) i(t)
v(t) = 10*heaviside(0.3-t);
fplot(v(t), [0 0.6])
L0=u0*pi*r^2*N^2;
L=L0/(x+(r*g/(2*W)));
Eqn1:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1233662/image.png)
The equation 2 has boundries, I can write in Mathmatica as,
-M*Dt[x[t], {t, 2}] - B*Dt[x[t], t] +
If[x[t] > xp2, -p2*(x[t] - xp2), 0] +
If[x[t] < xp1, -p1*(x[t] - xp1), 0] - k*(x[t] - x0) +
0.5*(i[t]*i[t]*D[L[x], x[t]]) = 0,
x[0] = xp2 - 0.00000001, x'[0] = 0., i[0] = 0.0
but I dont know how to write the second equation in matlab and solving and plotting for i(t) and x(t).
7 Comments
Torsten
on 16 Dec 2022
When I coded in mathmatica I used different names for them and in matlab I used different names.
Why ? Don't make life harder than it needs to be.
Accepted Answer
Torsten
on 16 Dec 2022
d=0.015;
xp1=0.002;
xp2=d-xp1;
tspan = [0 0.17];
y0 = [xp2 - 0.00000001;0;0];
options = odeset('RelTol',1e-12,'AbsTol',1e-12);
[T,Y] = ode15s(@fun,tspan,y0,options);
figure(1)
plot(T,Y(:,1))
figure(2)
plot(T,Y(:,2))
figure(3)
plot(T,Y(:,3))
function dy = fun(t,y)
u0=4*pi*10e-7;
r=0.01;
N=200;
g=0.001;
W=0.02;
M=0.3;
B=40;
R = 0.8;
d=0.015;
xp1=0.002;
xp2=d-xp1;
p2=1000000;
p1=1000000;
k=300;
x0=0.025;
L0=u0*pi*r^2*N^2;
x = y(1);
xp = y(2);
i = y(3);
L=L0/(x+(r*g/(2*W)));
dLdx = -L0/(x+(r*g/(2*W)))^2;
ToAdd = 0.0;
if x < xp1
ToAdd = -p1*(x - xp1);
elseif x > xp2
ToAdd = -p2*(x - xp2);
end
V0 = 0.0;
if t <= 0.3
V0 = 10;
end
dy = zeros(3,1);
dy(1) = y(2);
dy(2) = (-B*y(2) + ToAdd - k*(x-x0) + 0.5*i^2*dLdx)/M;
dy(3) = (V0 - i*dLdx*xp - R*i)/L;
end
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