Solve x′′ = −x − α(x2 − 1)x′, 0 ≤ t ≤ 30, with the initial conditions x(t = 0) = 0.5 and x′(t = 0) = 0, using RK4 method in your computer where α = 1. Plot the solution.

Question

KAUSHIK JAS 2019-9-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/480130-solve-x-x-x2-1-x-0-t-30-with-the-initial-conditions-x-t-0-0-5-and-x-t-0

回答： KAUSHIK JAS 2019-9-22

Urgent. Please solve it with explanation as soon as possible.

3 个评论
显示 1更早的评论隐藏 1更早的评论

KAUSHIK JAS 2019-9-12

编辑：KAUSHIK JAS 2019-9-12

I am a beginner of matlab.Not able to write this code. If you can do then answer it.

James Tursa 2019-9-12

编辑：James Tursa 2019-9-12

There are many people on this forum that can write the code for this, but we don't do that for homework problems. You must show some effort first, and then we can help you solve your coding problems. To code an RK4 scheme from scratch, I would first suggest you look at the equations here and try to code them up:

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods

The RK4 equations are spelled out. Just remember that your "y" and "k"s will be 2-element vectors since you have a 2nd order ODE to solve.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

KAUSHIK JAS 2019-9-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/480130-solve-x-x-x2-1-x-0-t-30-with-the-initial-conditions-x-t-0-0-5-and-x-t-0#answer_392959

I solve it correctly by my own. It is in below.

%RK2 of two variables

h=0.5;

t=0:h:30;

x=zeros(1,length(t));

z=zeros(1,length(t));

alpha=1.0;

x(1)=0.5;

z(1)=0;

f=@(p,q,r) (r);

g=@(p,q,r) (-q-alpha*(q^2-1)*r);

for i=1:(length(t)-1)

k11=h*f(t(i),x(i),z(i));

k12=h*g(t(i),x(i),z(i));

k21=h*f(t(i)+0.5*h,x(i)+0.5*k11,z(i)+0.5*k12);

k22=h*g(t(i)+0.5*h,x(i)+0.5*k11,z(i)+0.5*k12);

k31=h*f(t(i)+0.5*h,x(i)+0.5*k21,z(i)+0.5*k22);

k32=h*g(t(i)+0.5*h,x(i)+0.5*k21,z(i)+0.5*k22);

k41=h*f(t(i)+h,x(i)+k31,z(i)+k32);

k42=h*g(t(i)+h,x(i)+k31,z(i)+k32);

x(i+1)=x(i)+(1/6)*(k11+2*k21+2*k31+k41);

z(i+1)=z(i)+(1/6)*(k12+2*k22+2*k32+k42);

end

subplot(2,1,1);

plot(t,x);

subplot(2,1,2);

plot(t,z);

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

Solve x′′ = −x − α(x2 − 1)x′, 0 ≤ t ≤ 30, with the initial conditions x(t = 0) = 0.5 and x′(t = 0) = 0, using RK4 method in your computer where α = 1. Plot the solution.

3 个评论
显示 1更早的评论隐藏 1更早的评论

回答（1 个）

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

另请参阅

类别

标签

Community Treasure Hunt

Solve x′′ = −x − α(x2 − 1)x′, 0 ≤ t ≤ 30, with the initial conditions x(t = 0) = 0.5 and x′(t = 0) = 0, using RK4 method in your computer where α = 1. Plot the solution.

3 个评论 显示 1更早的评论隐藏 1更早的评论

回答（1 个）

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

另请参阅

类别

标签

Community Treasure Hunt

3 个评论
显示 1更早的评论隐藏 1更早的评论

0 个评论
显示 -2更早的评论隐藏 -2更早的评论