How to solve " Error using vertcat Dimensions of arrays being concatenated are not consistent " problem ?

I am getting "Error using vertcat Dimensions of arrays being concatenated are not consistent" error for the following code. Would anyone please help me find what is the problem here and how to fix it please.

clc
clear
close all

T_ar=300;                                          % Temparature of Argon gas
n=1.72e16;                                         % plasma density in m^-3
m_e=9.109e-31;                                     % mass of an electron in kg
e=1.60217663e-19;                                  % electronic charge in Coulomb
epsilon=8.854e-12;                                 % permittivity of free space in F*m^-1
A_sp=0.00502656;                                   % Powered Electrode Area in m^2 (4 cm radious)
A_sg=0.007854;                                     % Grounded Electrode Area in m^2 (5 cm radious)
lp=0.06;                                           % plasma bulk length in m

T_e=2.64;                                          % Electron Temparature in eV
p=60*10^-3;                                        % pressure in Torr
n_g=3.3*10^22*p;                                   % gas density in m^-3       
Km=10^-13;                                         % rate coefficient
v_m=Km*n_g;                                        % momentum transfer collision frequency
k_B=1.380649e-23;                                  % Boltzmann's Constant in J/K
v_e = sqrt(8*e*T_e/(pi*m_e));                      % mean thermal speed
v_eff=v_m+((v_e)/lp);                              % effective collision frequency


m_i=40;                                            % Argon mass in amu for determining bohm velocity
amu=1.660539e-27;                                  % 1 Dalton
v_B=sqrt((e*T_e)/(m_i*amu));                       % Bohm velocity

xx1=(1/(2*e*epsilon*n*A_sp^2));
xx2=(1/(2*e*epsilon*n*A_sg^2));
xx3=(1/(2*e*epsilon*n*A_sp^2*T_e));
xx4=(1/(2*e*epsilon*n*A_sg^2*T_e));
Lp=  (lp*m_e)/(e^2*n*A_sp);                        % Plasma Bulk Inductance
Lp_inv=1/Lp;


J_e=e*n*v_e;                                       % Coefficient of electron current
J_i=e*n*v_B;                                       % Coefficient of ion current
Jip=J_i*A_sp;                                      % Ion current at Powered Sheath
Jig=J_i*A_sg;                                      % Ion current at Grounded Sheath
Jep=J_e*A_sp;
Jeg=J_e*A_sg;

V0=300;                                            % Amplitude of RF input voltage
C_B=3.34e-6;                                       % Dc blocking capacitor
Cb_inv=1/C_B;


f = @(t,x) [-(x(4))-(Jip) + (Jep.*exp(-(xx1.*(x(1)^2))));
            (x(4))-(Jig) + (Jeg.*exp(-(xx2.*(x(2)^2))));
           -(Cb_inv.*(x(4)));
           (V0.*cos(t).*(Lp_inv))+(xx3.*(x(1)^2).*(Lp_inv))-(xx4.*(x(2)^2).*(Lp_inv))+(x(3).*(Lp_inv)) -(v_eff.*(x(4)))];

options = odeset('RelTol',1e-4,'AbsTol',1e-6);
[t,xa] = ode45(f,[0, 80],[0,0,-62,0],options);

Error using vertcat
Dimensions of arrays being concatenated are not consistent.

Error in solution>@(t,x)[-(x(4))-(Jip)+(Jep.*exp(-(xx1.*(x(1)^2))));(x(4))-(Jig)+(Jeg.*exp(-(xx2.*(x(2)^2))));-(Cb_inv.*(x(4)));(V0.*cos(t).*(Lp_inv))+(xx3.*(x(1)^2).*(Lp_inv))-(xx4.*(x(2)^2).*(Lp_inv))+(x(3).*(Lp_inv)),-(v_eff.*(x(4)))] (line 49)
f = @(t,x) [-(x(4))-(Jip) + (Jep.*exp(-(xx1.*(x(1)^2))));

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 104)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

figure(1)
plot(t,xa(:,1),'Color','blue')
title('xa1')
xlabel('t'), ylabel('Qsp (Powered Electrode Sheath Charge)')
grid on

figure(2)
plot(t,xa(:,2),'Color','blue')
title('xa2')
xlabel('t'), ylabel('Qsp (Grounded Electrode Sheath Charge)')
grid on

figure(3)
plot(t,xa(:,3),'Color','blue')
title('xa3')
xlabel('t'), ylabel('Self Bias Voltage')
grid on

figure(4)
plot(t,xa(:,4),'Color','blue')
title('xa4')
xlabel('t'), ylabel('Plasma Current')
grid on

Answer 1

[Stephen23]

You probably think that your square brackets are creating a 4x1 vector.

But they aren't, because of the random space characters that you included around the plus & minus operators: you need to be consistent: either all operators with spaces or none of them (simplest is none). This will fix your bug:

(V0.*cos(t).*(Lp_inv))+(xx3.*(x(1)^2).*(Lp_inv))-(xx4.*(x(2)^2).*(Lp_inv))+(x(3).*(Lp_inv))-(v_eff.*(x(4)))];

% ^ no space

Compare the effect of the space around the minus operator here:

[1 2 -3] % what you did

ans = 1×3

1 2 -3

[1 2-3] % what you should do

ans = 1×2

1 -1

[1 2 - 3] % best avoided

ans = 1×2

1 -1

Also you should get rid of most of those parentheses, they make the code hard to follow (which in turn makes it harder to debug). For example this:

-(x(4))-(Jip) + (Jep.*exp(-(xx1.*(x(1)^2))))

should be simply:

-x(4)-Jip+Jep.*exp(-xx1.*x(1).^2)

[Golam]

@Stephen23 great, it works

[Golam]

@@Stephen23 I used all those parenthesis in an attempt to solve the error I was having .