Plotting a multivariable function, that also has a summation
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Good Afternoon everyone,
I am attempting to plot the funtion above in matlab, I have been trying with symsum, for loops & 3D plots but can't get it to work. Hopefully someone can help me!
Thank you
采纳的回答
xstart = 0.0;
xend = 1.0;
nx = 100;
tstart = 0.0;
tend = 5.0;
nt = 100;
nsum = 31;
X = linspace(xstart,xend,nx);
T = linspace(tstart,tend,nt);
U = zeros(nx,nt);
for ix = 1:nx
x = X(ix);
for it = 1:nt
t = T(it);
for isum = 1:2:nsum
U(ix,it) = U(ix,it) + ?
end
end
end
U = U * 400/pi^3;
surf(X,T,U)
3 个评论
Ali Mosa
2022-12-11
Thanks so much for the help, I just wanted to ask about the use of nx and nt. Why there is two separate variables since they appear to do the same thing, so which would take the place of n in the equation for U(ix,it)?
Also the value chosen for nsum, is that random?
Sorry for all the questions, I want to make sure I understand this so I can apply these techniques in other problems I come across!
You have two dimensions in your equation: x in space and t in time.
Both dimensions are independent from each other.
So you need two loops to calculate values for U depending on a given value of x (this is the loop with ix) and a given value of t (this is the loop with it) simultaneously, thus for a pair (X(ix),T(it)).
The value U(ix,it) at X(ix) and T(it) is given by an infinite series. Thus you need a third loop over the number of elements of the series you want to account for. This is the loop with isum. If you feel better then, you can replace isum by n. For simplicity, I chose a fixed value for the number of elements of the series that are summed (31) (independent of x and t). Usually, this is done by evaluating the size of the series elements and a stopping criterion for each pair (X(ix),T(it)) separately.
Ali Mosa
2022-12-11
更多回答（1 个）
Hi Ali,
Another approach that you might be interested in, which is less code but requires more memory, is to use an anonymous function
u = @(x,t,N) 400/pi^3*sum(sin(pi*reshape(1:2:N,1,1,[]).*x).*exp(-reshape(1:2:N,1,1,[]).^2.*pi^2.*0.003.*t)./reshape(1:2:N,1,1,[]).^3,3);
[X,T] = meshgrid(0:.1:1);
Nsum = 31; % uppler limit on the n-summation
surf(X,T,u(X,T,Nsum))
Memory could be reduced by loop-summing u over scalar values of n for a fixed set of values of X and T
U = 0*X;
for n = 1:2:31
U = U + u(X,T,n);
end
surf(X,T,U)
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