How to plot a three variable complex function

Question

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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

%---------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

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

%----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);