How to find value of z from the mesh/surface plot when values of x and y are given?

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CY
CY 2012-9-14
评论： Nathalie 2014-3-20
Through matlab i use finite-difference method to solve standard dispersal equation with initial condition and boundary condition. A mesh/surface plot is then produced. Now, from the mesh/surface plot, how to find the value of z when values of x and y are given?

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回答（1 个）

Javier
Javier 2012-9-14
Hello CY
Im going to use the following function (it comes in Matlab help/mesh function).
%Function
[X,Y] = meshgrid(-8:.5:8); %Arbitrary values
R = sqrt(X.^2 + Y.^2) + eps;
Z = sin®./R; %Z is function of X and Y
mesh(Z);
If you want to find the value of Z at X=5 and Y=4, just evalueta the function Z in that point. This mean that you have to evaluate first in R to get the Z desired result (also work for vectors).
NewR=feval(@(xx,yy)[sqrt(xx.^2 + yy.^2)],5,4)
Newz=feval(@(NewR)[sin(NewR)./NewR],NewR)
Hope it helps.
Best regards and if solve your question please grade.
Javier
  2 个评论
CY
CY 2012-9-17
Thank you very much for your reply. However, how about for problem where there's no analytical solution? My problem sound sth like this: The model of dispersal: du/dt=D*(d^2u/dx^2) for t>=0 and x>=0. The initial condition is u(x,0)= -0.0013*(x^2)+0.5673*x+58.1554 for x<=t<=11. The boundary condition is u(0,t)=0 and u(13,t)=0 for 0<=x<=13. By using matlab i obtained numerical solution (using explicit finite-difference method) in the form of a mesh plot. Now, with that mesh plot, i don't know how to obtain the value of, say u(5,6), from the mesh plot. Thank you very much.

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