Need to solve this with Runge-Kutta 4th order method in MatLab.

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Cubii4
Cubii4 2022-11-10
移动：Cris LaPierre 2022-11-28
y''-μ(1-y^2)*y'+y=0
y(x=0)=1 ; y'(x=0)=0
μ=0; 0.2; 1; 5 and 10 (for each value a different result)
y'(x) versus y(x) and x versus y(x) functions plot in the range [0; 50].
  2 个评论
James Tursa
James Tursa 2022-11-17
What have you done so far? What specific problems are you having with your code?
Cubii4
Cubii4 2022-11-27
fy=@(x,y,z) z;
fz=@(x,y,z) (1-y^2)*z-y;
x(1)=0;
z(1)=0;
y(1)=1;
h=1;
xfinal=10;
N=ceil((xfinal-x(1))/h);
for j=1:N:xfinal
x(j+h)=x(j)+h;
k1y=fy(x(j),y(j),z(j));
k1z=fz(x(j),y(j),z(j));
k2y=fy(x(j)+h/2,y(j)+h/2*k1y,z(j)+h/2*k1z);
k2z=fz(x(j)+h/2,y(j)+h/2*k1y,z(j)+h/2*k1z);
k3y=fy(x(j)+h/2,y(j)+h/2*k2y,z(j)+h/2*k2z);
k3z=fz(x(j)+h/2,y(j)+h/2*k2y,z(j)+h/2*k2z);
k4y=fy(x(j)+h,y(j)+h*k3y,z(j)+h*k3z);
k4z=fz(x(j)+h,y(j)+h*k3y,z(j)+h*k3z);
y(j+h)=y(j)+h/6*(k1y+2*k2y+2*k3y+k4y);
z(j+h)=z(j)+h/6*(k1z+2*k2z+2*k3z+k4z);
end
x = 1:N:xfinal;
figure;
plot(x,y,z,'LineWidth',2);
xlabel('X');
ylabel('Y');
I took out the μ value and decreased the range to (0,10) just until I can understand how to form the code and this is what I have done but there is a problem with the plot. Can I get some help with it. Thanks.

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采纳的回答

Torsten
Torsten 2022-11-27
移动：Cris LaPierre 2022-11-28
Ran in:
fy=@(x,y,z) z;
fz=@(x,y,z) (1-y^2)*z-y;
x(1)=0;
z(1)=0;
y(1)=1;
h=0.1;
xfinal=10;
N=ceil((xfinal-x(1))/h);
for j=1:N
x(j+1)=x(j)+h;
k1y=fy(x(j),y(j),z(j));
k1z=fz(x(j),y(j),z(j));
k2y=fy(x(j)+h/2,y(j)+h/2*k1y,z(j)+h/2*k1z);
k2z=fz(x(j)+h/2,y(j)+h/2*k1y,z(j)+h/2*k1z);
k3y=fy(x(j)+h/2,y(j)+h/2*k2y,z(j)+h/2*k2z);
k3z=fz(x(j)+h/2,y(j)+h/2*k2y,z(j)+h/2*k2z);
k4y=fy(x(j)+h,y(j)+h*k3y,z(j)+h*k3z);
k4z=fz(x(j)+h,y(j)+h*k3y,z(j)+h*k3z);
y(j+1)=y(j)+h/6*(k1y+2*k2y+2*k3y+k4y);
z(j+1)=z(j)+h/6*(k1z+2*k2z+2*k3z+k4z);
end
figure;
plot(x,[y;z],'LineWidth',2);
xlabel('X');
ylabel('Y');

更多回答（1 个）

Cris LaPierre
Cris LaPierre 2022-11-10
  1 个评论
Cubii4
Cubii4 2022-11-27
I still have some problems with the plot. I wrote the code in the comment above if I can get some help with it. Thanks.

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