How do I plot a solution from a PDE within a unit square?
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I have solved a nonlinear PDE but now need to plot the solution as a line plot rather than as a surface plot. The solution matrix is given as (phi0) and the unit square is of x and y dimension. How do I obtain a line plot of the solution within this unit square ? see attached for something similar of what i intend doing.
clear;
clc
% initialise number of nodes
L=1;
H=1;
M=10; % number of x nodes
N=10;
dx=L/(M-1);
dy=H/(N-1);
x=linspace(0,L,M); % discreet x values
y=linspace(0,H,N);
% initialise Guess
phi0=ones(M,N)*0.5
%Boundary conditions phi0(1,:)=0; % bottom boundary
phi0(M,:)=1;% right boundary
phi0(:,1)=0; %left boundary
phi0(:,N)=1; % top boundary
% initialise Guess
phi_delta=ones(M,N)*0.5 %zeros(M,N);
% initialise Boundary conditions
phi_delta0(1,:)=0; % bottom boundary
phi_delta0(M,:)=1;% right boundary
phi_delta0(:,1)=0; %left boundary
phi_delta0(:,N)=1; % top boundary
Tol=10^-6;
Tol1=10^-6;
flag1=2
while flag1==2
flag1=0;
flag = 1;
while flag==1
flag =0;
phi_delta=phi_delta0
for i=2:M-1
for j=2:N-1
f(i,j)=((phi0(i+1,j)^2-phi0(i-1,j)^2)/2*dx)+((phi0(i,j+1)^2-phi0(i,j-1)^2)/2*dy)-((phi0(i+1,j)-2*phi0(i,j)+phi0(i-1,j)/dx^2)+...
(phi0(i,j+1)-2*phi0(i,j)+phi0(i,j+1)/dy^2))-1/2*((phi0(i+1,j)^2-2*phi0(i,j)^2+phi0(i-1,j)^2/dx^2)...
+(phi0(i,j+1)^2-2*phi0(i,j)^2+phi0(i,j-1)^2/dy^2));
aE=(phi0(i+1,j)/dx)-((1+phi0(i+1,j))/dx^2);
aW=(-phi0(i-1,j)/dx)-((1+phi0(i-1,j))/dx^2);
aN=(phi0(i,j+1)/dy)-((1+phi0(i,j+1))/dy^2);
aS=(-phi0(i,j-1)/dy)-(1+phi0(i,j-1))/dy^2;
a0=(2*(1+phi0(i,j))/dx^2)+(2*(1+phi0(i,j))/dy^2);
phi_delta0(i,j)=(-f(i,j)-aE*phi_delta(i+1,j)-aW*phi_delta(i-1,j)-aN*phi_delta(i,j+1)-aS*phi_delta(i,j-1))/a0
error = abs((phi_delta0(i,j)-phi_delta(i,j))/phi_delta(i,j));
if error > Tol
flag=1
end
end
end
end
phi0=phi0+0.05*(phi_delta0)
if error > Tol1
flag1=2
end
end
%Boundary conditions
phi0(1,:)=0; % bottom boundary
phi0(M,:)=1;% right boundary
phi0(:,1)=0; %left boundary
phi0(:,N)=1; % top boundary
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