Compare results of different step size using Euler's method
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x1=zeros(10000,1);
x2=zeros(10000,1);
x3=zeros(10000,1);
Time=zeros(10000,1);
for i=1:10001
t=(i-1)*0.0005;
Time(i)=t;
if t==0
x1(i)=0;
x2(i)=0;
x3(i)=2;
else
x1(i)=x1(i-1)+x2(i-1)*0.0005;
x3(i-1)=2-9*sin(x1(i-1))-x2(i-1);
x2(i)=x2(i-1)+x3(i-1)*0.0005;
end
Xa=x1*180/pi;
plot(Time,Xa,'red')
I can get the plot for one time interval but I want to get it for different time intervals such as at 0.001, 0.01,0.1 and also compare the results on the same plot. how do i do this? please help??
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采纳的回答
ME
2019-10-30
I have made a few tweaks to your code and it will now allow you to alter one parameter value (the time step size) and produce a new approximation that will be added to your previous plot.
clear all
h = 0.00001;
x1=zeros(round(5/h),1);
x2=zeros(round(5/h),1);
x3=zeros(round(5/h),1);
Time=zeros(round(5/h),1);
for i=1:(5/h)+1
t=(i-1)*h;
Time(i)=t;
if t==0
x1(i)=0;
x2(i)=0;
x3(i)=2;
else
x1(i)=x1(i-1)+x2(i-1)*h;
x3(i-1)=2-9*sin(x1(i-1))-x2(i-1);
x2(i)=x2(i-1)+x3(i-1)*h;
end
end
Xa=x1*180/pi;
hold on
plot(Time,Xa)
Here h is your time step and I have just modified everything else to produce the correct length arrays for storing the results. I also took out the 'red' from your plotting command so that each approximation will automatically plot in a different colour.
2 个评论
ME
2019-10-30
编辑:ME
2019-10-30
I guess you'd have to adjust this to something like:
h = sort([0.00001 0.005 0.01],'descend');
for step = 1:numel(h)
x1=zeros(round(5/h(step)),1);
x2=zeros(round(5/h(step)),1);
x3=zeros(round(5/h(step)),1);
Time=zeros(round(5/h(step)),1);
for i=1:(5/h(step))+1
t=(i-1)*h(step);
Time(i)=t;
if t==0
x1(i)=0;
x2(i)=0;
x3(i)=2;
else
x1(i)=x1(i-1)+x2(i-1)*h(step);
x3(i-1)=2-9*sin(x1(i-1))-x2(i-1);
x2(i)=x2(i-1)+x3(i-1)*h(step);
end
end
Xa=x1*180/pi;
hold on
plot(Time,Xa)
end
Here the sort is to make sure that you start with the largest step size, otherwise you'll run into issues when you come to plotting.
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