How to solve a partial derivative equation in MATLAB?

Hello, orgininally I solved this set of differential equations using Euler's method:

they were solved with this:

for i=1:1:500000
    
    t(i+1)=t(i)+dt;
    u(i+1) = u(i)+ dt*((1/e)*((k*u(i)*(u(i)-a)*(1-u(i)))-v(i)));
    v(i+1) = v(i)+ dt*(u(i)-v(i));
      
end    

Now I have a similar set of equations as shown below:

Can anyone explain how I might go about adjusting my code to solve for this partial derivative in the new equations? Thank you so much!

Here is the full source code:

%Clear command window and workspace
clear 
close all
clc

% Fitzhugh-Nagoma model parameters
e=0.03; k=3; a=0.05; 
i = 0.001;

figure(1);
hold on

u=zeros(100000,1);
v=zeros(100000,1);
t=zeros(100000,1);

% Initial conditions:
u(1)=0.6;
v(1)=0.0;

t(1)=0;
dt=0.001;

%==========================================================================
% Forvard Euler Method, for soluing the ODE
%==========================================================================

for i=1:1:500000
    
    t(i+1)=t(i)+dt;
    u(i+1) = u(i)+ dt*((1/e)*((k*u(i)*(u(i)-a)*(1-u(i)))-v(i)));
    v(i+1) = v(i)+ dt*(u(i)-v(i));
      
end

% Getting the plot

figure(1);
plot(t,u)
legend('u','Trajectory')
title('Time Series Plot')
xlabel('Time')
ylabel('u')
xlim([0 5])

Answer 1

[Torsten]

Use "pdepe".

Best wishes

Torsten.