How to solve and plot system of nonlinear differential equations?

1 次查看（过去 30 天）

显示更早的评论

berk26092 2022-12-16

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1879907-how-to-solve-and-plot-system-of-nonlinear-differential-equations

评论： Torsten 2022-12-16

采纳的回答： Torsten

在 MATLAB Online 中打开

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:

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 个评论
显示 5更早的评论隐藏 5更早的评论

berk26092 2022-12-16

Sorry... When I coded in mathmatica I used different names for them and in matlab I used different names. I think now the question should be all clear.

Torsten 2022-12-16

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.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Torsten 2022-12-16

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1879907-how-to-solve-and-plot-system-of-nonlinear-differential-equations#answer_1129797

在 MATLAB Online 中打开

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

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

berk26092 2022-12-16

Thank you!

请先登录，再进行评论。

类别

MATLAB Mathematics Numerical Integration and Differential Equations Ordinary Differential Equations

在 Help Center 和 File Exchange 中查找有关 Ordinary Differential Equations 的更多信息

产品

MATLAB

版本

R2022b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by