How to solve 'Index number exceeds number of array elements(1)'

function substrate_glucose()

% Effect of carbon sources on the growth of Lactoccus lactis. Ibrahim et. al (2010)
% Parameters
u = 0.57 ; % specific growth rate h-1 
y = 0.52 ; % cell yield coefficient (g/g)
s = 5.12 ; % substrate utilization

% Initial Value
x0 = 0.3 ;      % Initial cell concentration (g/L)
XSOL(1) = x0 ;  % Store initial value in solution vector
X = x0 + y*s ;  % Calculated maximum X
s0 = 10 ;       % Initial carbon source
SSOL(1) = s0 ;  % Store initial value of s

% Time information
dt = 1 ;         % Time step
TFinal = 8 ;    % Final simulation time
t=0 ;            % Initialize time to zero
tVec(1) =0;      % store first time-value      

% Solve equation/ March forward in time
ct = 1 ;    % counter
while t < TFinal
    
    % Euler's time-step
    SSOL(ct+1) = SSOL(ct) - dt*u*(1/y)*(XSOL(ct)*(1-XSOL(ct)/X));
    
    % Store time-value
    tVec(ct+1) = t + dt;
    
    % Update counter and time
    t = t+dt ; 
    ct = ct+1 ;  
end

got error in SSOL(ct+1) = SSOL(ct) - dt*u*(1/y)*(XSOL(ct)*(1-XSOL(ct)/X)); where it exceeds the number of array elements (1).

Can someone please help me?

Answer 1

[Alan Stevens]

You don't update XSOL, so when ct is 2, XSOL(ct) doesn't exist.

[Siti Humaira Mohd Jasni]

understood. do you have any suggestion to solve the problem?

[Alan Stevens]

You need an equation that updates XSOL.

[Siti Humaira Mohd Jasni]

I have seperate the XSOL and update it like this,

XSOL(ct+1) = XSOL(ct) + dt*u*XSOL(ct)*(1-XSOL(ct) / X);

but I'm not sure how to use it for SSOL.

[Image Analyst]

Just have a for loop in advance of your while loop where you create XSOL

for ct = 1 : tFinal-1
    XSOL(ct+1) = XSOL(ct) + dt*u*XSOL(ct)*(1-XSOL(ct) / X);
end

[Siti Humaira Mohd Jasni]

ct = 1 ;    % counter
for ct = 1 : TFinal-1
    XSOL(ct+1) = XSOL(ct) + dt*u*XSOL(ct)*(1-XSOL(ct) / X);
end
while t < TFinal

    SSOL(ct+1) = SSOL(ct) - dt*u*(1/y)*XSOL(ct);
   
end

I did it like this but it still have error at SSOL(ct+1) = SSOL(ct) - dt*u*(1/y)*XSOL(ct);

index exceed the number of arrays.

[Alan Stevens]

Like this:

% Effect of carbon sources on the growth of Lactoccus lactis. Ibrahim et. al (2010)
% Parameters
u = 0.57 ; % specific growth rate h-1 
y = 0.52 ; % cell yield coefficient (g/g)
s = 5.12 ; % substrate utilization

% Initial Value
x0 = 0.3 ;      % Initial cell concentration (g/L)
XSOL(1) = x0 ;  % Store initial value in solution vector
X = x0 + y*s ;  % Calculated maximum X
s0 = 10 ;       % Initial carbon source
SSOL(1) = s0 ;  % Store initial value of s

% Time information
dt = 1 ;         % Time step
TFinal = 8 ;    % Final simulation time
t=0 ;            % Initialize time to zero
tVec(1) =0;      % store first time-value      

% Solve equation/ March forward in time
ct = 1 ;    % counter

ct = 1 ;    % counter
for ct = 1 : TFinal-1
    XSOL(ct+1) = XSOL(ct) + dt*u*XSOL(ct)*(1-XSOL(ct) / X);
    SSOL(ct+1) = SSOL(ct) - dt*u*(1/y)*XSOL(ct);
        
    % Store time-value
    tVec(ct+1) = t + dt;
    
    % Update counter and time
    t = t+dt ; 
    ct = ct+1 ;  

end
subplot(2,1,1)
plot(tVec,XSOL),grid
xlabel('t'), ylabel('XSOL')
subplot(2,1,2)
plot(tVec,SSOL),grid
xlabel('t'), ylabel('SSOL')