i need help with this question

2019 5 7
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更新时间：2019 5 7
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I am supposed to find the number of timesteps i.e the number of steps taken but my answer is incorrect any inputs on my code will be a major help thanks.Also has the advection equation with the center spaced method used correctly ?
N=200;
x=linspace(-10,10,N);
dx=x(2)-x(1);
c=-0.9;
t=0;
dt=0.2;
timestep=0;
f=@(x)exp(-5*x.^2);
y=f(x)';
figure(1),plot(x,y)
title(['Current time=',num2str(t)])
drawnow
%using centered space
A=eye(N)-(0.5*c*(dt/dx))*((diag(ones(N-1,1),1)-diag(ones(N,1),0)));
while abs(y(end))<0.001 && abs(y(1))<0.001
y=A*y;
t=t+dt;
timestep=timestep+1;
figure(1),cla
plot(x,y)
hold on
plot(x,f(x-c*t),'r')
title(['Current time=',num2str(t)])
drawnow
end

6 个评论
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Jan
Jan 2019-5-7
编辑：Jan 2019-5-7
All we know is the code. We cannot know, why you assume, that the answer is wrong. Without any further details it is impossible to miodify a code, such that it produces the output you expect. So please edit the question, exoplain, which problem you want to solve and why you assume, that there is a bug.
dulanga
dulanga 2019-5-7
with c= -0.9 on -10<x<10 with the Gaussian initial condition f,The code runs from t = 0 until a time in which |y|=0.001 on one of the boundaries,solve this problem using the centred-in-space approximation
So my assignment has a method of checking if my answer is correct where input my final answer and it says if it is correct or not and in this case it is incorrect.
the below is the centered approach method i should implement in matlab
thanks
Cap22222ure.JPG
Torsten
Torsten 2019-5-7
编辑：Torsten 2019-5-7
A is wrong. The factor 0.5 is missing, and the lower diagonal is replaced by a main diagonal.
Maybe this A was written for Euler forward instead of centered.
dulanga
dulanga 2019-5-7
编辑：dulanga 2019-5-7
oh sorry i forgot the 0.5 where the c is at what do u mean by lower diagonal is replaced by main ?
%using centered space
A=eye(N)-(0.5*c*(dx/dt))*diag(ones(N-1,1),1)-diag(ones(N-1,1),-1);
Torsten
Torsten 2019-5-7
编辑：Torsten 2019-5-7
You forgot the parenthesis around the difference of the diag-expressions.
And it must be dt/dx instead of dx/dt.
dulanga
dulanga 2019-5-7
thanks alot how would u implemnt this Capture.JPG
Capt11ure.JPG
N=1000;
x=linspace(-10,10,N);
dx=x(2)-x(1);
c=2.6;
t=0;
dt=0.2;
timestep=0;
f=@(x)exp(-5*x.^2);
y=f(x)';
figure(1),plot(x,y)
title(['Current time=',num2str(t)])
drawnow
%using lax
A=eye(N)-(0.5*c*(dt/dx))*diag(ones(N-1,1),1)-diag(ones(N-1,1),-1);
while abs(y(end))<0.001 && abs(y(1))<0.001
y=A*y;
t=t+dt;
timestep=timestep+1;
figure(1),cla
plot(x,y)
hold on
plot(x,f(x-c*t),'r')
title(['Current time=',num2str(t)])
drawnow
end

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dulanga
dulanga
2019-5-7

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2019-5-7

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