How to solve a partial derivative equation in MATLAB?

Question

Westin Messer 2018-11-24

0
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https://ww2.mathworks.cn/matlabcentral/answers/431690-how-to-solve-a-partial-derivative-equation-in-matlab

回答： Torsten 2018-11-26

在 MATLAB Online 中打开

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])