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

2 views (last 30 days)
CY on 14 Sep 2012
Commented: Nathalie on 20 Mar 2014
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?

Javier on 14 Sep 2012
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.
Javier
CY on 17 Sep 2012
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 on 20 Mar 2014