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

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CY 2012-9-14

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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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Answer 1

Javier 2012-9-14

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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

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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.

Nathalie 2014-3-20