MATLAB: WHAT TO GRAPH USING ELEMENTWISE MULTIPLCATION

elementwise multiplication

i WANT TO PLOT THE GRAPH FOR

U(X,T)=EXP(-4*PI^2*0.5*y)*SIN(2*PI*x)

AS PER THE SUGGESTION GIVEN ON MATHWORK I WROTE THIS CODE BUT STILL GRAPH IS NOT CORRECT. i AM USING R2013 VERSION OF MATLAB. pROVIDE SOME MORE EXAMPLE.

x = linspace(0,1 ,51)';
y = linspace(0,1,51)';
[X, Y] = meshgrid(x, y);
Z=exp(-4.*(pi^2)*0.5*Y)*sin(2*pi*X);
surf(X, Y, Z);
ylabel('t');
xlabel('x');
zlabel('u(x,t)')

Best Answer

It works perfectly for me, exactly like I showed you before, (but you ignored):

x = linspace(0,1 ,51)';
y = linspace(0,1,51)';
[X,Y] = meshgrid(x, y);
Z = exp(-2*pi^2*Y).*sin(2*pi*X); % I only changed this line!
surf(X, Y, Z);
ylabel('t');
xlabel('x');
zlabel('u(x,t)')

Lets have a look, so you can understand why that line. You wrote this:

Z=exp(-4.*(pi^2)*0.5*Y)*sin(2*pi*X);
        ^ element-wise multiply, but pointless.

But what is the point of element-wise multiplication with 4? 4 is a scalar number and so is pi, it serves no purpose whatsoever to use element-wise multiplication with them. So what parts of that calculation are not scalar? Answer: X and Y. Therefore any operation involving X and Y, or any other arrays derived from them will need to use element-wise operations. In this case this means the exp(..) and sin(..) terms will need to be multiplied using element-wise multiply. And thus I showed you (twice so far) this, which uses element-wise multiply for the terms that are arrays (and I did not use it on the scalar values like you did):

exp(-2*pi^2*Y).*sin(2*pi*X)
              ^ element-wise multiply, required.

or if you really want to have that 4 and 0.5:

exp(-4*pi^2*0.5*Y).*sin(2*pi*X)

You have now been told this multiple times:

https://www.mathworks.com/matlabcentral/answers/343257-x-linspace-10-10-51-y-linspace-0-0-3-51-x-y-meshgrid-x-y-z-x-1-y-surf-x-y#answer_269503

https://www.mathworks.com/matlabcentral/answers/343230-i-wrote-the-code-to-plot-two-dimension-graph-but-it-is-not-showing-the-correct-graph-so-can-you-chec#answer_269488

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