How to plot a three variable complex function

I want to plot two functions : the first one is the exact solution of a 2D time dependent PDE, and the second one is the solution of the PDE using the finite difference method.

I tried using fimlicit3() but an error message is showing also the plot is empty.

clc ; clear all ; close all ;
% 2D time dependent linear PDE in the domain [0 , l ] x [0 , l ]
% iut =  -( uxx + uyy) + u 
% Initial condition u(x,y,0) = phi(x,y)
% Boundary conditions u(0,0,t) = u(0,0,l) = 0 
% Approximate solution by using explicit FDS

N = 4;      % space discretization
P = 9;      % time discretization
l = pi;     % the space interval [0,l]x[0,1]
T = 1;      % the time interval [0,T]
h = l/(N+1); % the space step (I used the same step for x and y)
k = T/(P+1); % the time step 
alpha = k/(h^2); % alpha and beta are coeficients used in the FD scheme
beta= 1-4*alpha-complex(0 ,1)*k;

%----The function phi(x,y)--------
phi=@(x,y) sin(10*x)*sin(4*y);
for r = 1:N+1
    for s = 1:N+1
    phirs(r,s) = phi((r-1)*h,(s-1)*h);
    end
end

%---------The function u---------
u = zeros(N+1,N+1,P+1);

%------Boundary connditions-----
for r = 1:N+1
    for s = 1:N+1
        u(r,s,1) = phirs(r,s);
    end 
end

u(1,1,1:P+1) = 0;
u(N+1,N+1,1:P+1) = 0;
%-------Finding u(i,j,n)------
for n = 1:P
    for i = 2:N
        for j = 2:N
            u(i,j,n+1)=  beta*u(i,j,n) + alpha*(u(i+1,j,n)+u(i-1,j,n)+u(i,j+1,n)+u(i,j-1,n));
        end
    end
end

%----The exact solution ----
f = @(x,y,t) exp(complex(0,1)*t)*sin(10*x)*sin(4*y);
%----The plot ------
t=linspace(0,1,1/10);
x=linspace(0,pi,1/5);
y=linspace(0,pi,1/5);
f = @(x,y,t) exp(complex(0,1)*t)*sin(10*x)*sin(4*y);
fimplicit3(u)

Error using nargin
Argument must be either a character vector, string scalar, or a function handle.

Error in matlab.graphics.function.ImplicitFunctionSurface>getFunction

Error in matlab.graphics.function.ImplicitFunctionSurface/updateFunction

Error in matlab.graphics.function.ImplicitFunctionSurface/set.Function_I

Error in matlab.graphics.function.ImplicitFunctionSurface/set.Function

Error in matlab.graphics.function.ImplicitFunctionSurface

Error in fimplicit3>singleFimplicit (line 186)
hObj = matlab.graphics.function.ImplicitFunctionSurface(fn,extraOpts{:},args{:});

Error in fimplicit3>@(f)singleFimplicit(cax,f,limits,extraOpts,args) (line 148)
hObj = cellfun(@(f) singleFimplicit(cax,f,limits,extraOpts,args),fn,'UniformOutput',false);

Error in fimplicit3>vectorizeFimplicit (line 148)
hObj = cellfun(@(f) singleFimplicit(cax,f,limits,extraOpts,args),fn,'UniformOutput',false);

Error in fimplicit3 (line 122)
hObj = vectorizeFimplicit(cax,fn,limits,extraOpts,args);

Answer 1

[Torsten]

You cannot plot the complete result of a function that depends on three independent variables.

But you can plot it on slices (i.e. 2d-objects in (x,y,t)-space (e.g. planes)):

https://uk.mathworks.com/help/matlab/ref/slice.html

And plot real part and imaginary part of the function separately (using real and imag).

[Aïda]

Thank you so much, this was really helpful.