Runge kutta 4th order method for Fitzhugh Nagumo model

So I wrote a runge kutta 4th order code, or what I believe to be one, to solve the fitzhugh-nagumo model equations I was given to solve. I am getting a left side is a 1x1 and the right side is a 2x2 at line 42. I may have done the runge kutta wrong, but I tried changing some things around to make it a 1x1 to a 1x1 but that gave even more errors. Any help would be greatly appreciated, thank you.

clear all

close all

eq1=@(t,x) FN(t,2,0.1,0.1,-0.1);

[x, t] = rk4(eq1,0);

v=x(:,1);

w=x(:,2);

figure(1)

plot(v)

hold on

plot(w)

function dvwdt = FN(~,a,L,e,I) %

x(1)=0; %initial condition for v

x(2)=0; %initial condition for w

v=x(1);

w=x(2);

dvwdt = [I-2*v^2+3*v^2-w; %dv/dt

e*(a*v-L-w)]; %dw/dt

end

function [x, t] = rk4(f, x0)

t0=0; %starting time

dt=0.01; %step size

tf=100; %ending time

t=t0:dt:tf;

nt=numel(t);

nx=numel(x0);

x=nan(nx,nt);

x(:,1)=x0;

for k=1:nt-1

k1= dt*f(t(k),x(:,k));

k2= dt*f(t(k)+dt/2,x(:,k)+k1/2);

k3= dt*f(t(k)+dt/2,x(:,k)+k2/2);

k4= dt*f(t(k)+dt,x(:,k)+k3);

dx=(k1+2*k2+2*k3+k4)/6;

x(:,k+1)= x(:,k)+dx;

end

end

Answer 1

[Benjamin Thompson]

Do you need to use x on the first line in the eq1 function that calls FN?

[Vezzaz]

I used x because I thought that is what is needed for a differential equation. Also the differential equation is dv/dt and dw/dt so i used dx/dt as a substitute for v and dy/dt as a substitute for w. Which just made things more confusing. But now that I look at it that, x is probably where I went wrong and I am going to try and fix it.