How can I input sum over in function depend on time?

Question

cindyawati cindyawati on 14 Jul 2023

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https://uk.mathworks.com/matlabcentral/answers/1996088-how-can-i-input-sum-over-in-function-depend-on-time

Edited: Torsten on 14 Jul 2023

Accepted Answer: Torsten

Open in MATLAB Online

I get error and the error is

Index exceeds the number of array elements (1). I want to write this equation (blue highlight)

this is my code

tstart = 0;
tend = 100;
dt = 0.01;
T = (tstart:dt:tend).';
Y0 = [10 0 0 0 0 0 0 0];
f = @myode;
Y = fRK4(f,T,Y0);
Index exceeds the number of array elements. Index must not exceed 1.

Error in solution>fRK4 (line 93)
     summ=K(i).*M(i);
M1 = Y(:,1);
M2 = Y(:,2);
M3 = Y(:,3);
M4 = Y(:,4);
M5 = Y(:,5);
M6 = Y(:,6);
O  = Y(:,7);
P  = Y(:,8);
figure
%subplot(3,1,1)
%hold on
plot(T,M1,'r','Linewidth',2) 
xlabel('Times (days)')
ylabel('M1 (gr/ml)')
figure
%subplot(3,1,2)
%hold on
plot(T,M2,'b','Linewidth',2)
xlabel('Times (days)')
ylabel('M2 (gr/ml)')
figure
%subplot(3,1,3)
%hold on
plot(T,M3,'g','Linewidth',2)
xlabel('Times (days)')
ylabel('M3 (gr/ml)')
figure
%subplot(3,1,3)
%hold on
plot(T,M4,'b--','Linewidth',2)
xlabel('Times (days)')
ylabel('M4 (gr/ml)')
figure
%subplot(3,1,3)
%hold on
plot(T,M5,'r--','Linewidth',2)
xlabel('Times (days)')
ylabel('M5 (gr/ml)')
figure
%subplot(3,1,3)
%hold on
plot(T,M6,'g--','Linewidth',2)
xlabel('times (days)')
ylabel('M6 (gr/ml)')
figure
%subplot(2,1,1)
%hold on
plot(T,O,'k','Linewidth',2)
xlabel('Times (days)')
ylabel('O (gr/ml)')
figure
%subplot(2,1,2) 
%hold on
plot(T,P,'m','Linewidth',2)
xlabel('Times (days)')
ylabel('P (gr/ml)')
function Y = fRK4(f,T,Y0)
  N = numel(T);
  n = numel(Y0);
  Y = zeros(N,n);
  Y(1,:) = Y0;
  for j = 2:N
    t = T(j-1);
    y = Y(j-1,:);
    h  = T(j) - T(j-1);
    k0 = f(t,y);
    k1 = f(t+0.5*h,y+k0*0.5*h);
    k2 = f(t+0.5*h,y+k1*0.5*h);
    k3 = f(t+h,y+k2*h);
    Y(j,:) = y + h/6*(k0+2*k1+2*k2+k3);
  end
     
    K=2;
    M=2;
    sum= zeros(1,6);
     for i = 2:6
     summ=K(i).*M(i);
     sum(i)=sum(i)+summ;
     end
end
function CM1 = myode (~,MM)
  M1 = MM(1);
  M2 = MM(2);
  M3 = MM(3);
  M4 = MM(4);
  M5 = MM(5);
  M6 = MM(6);
  O  = MM(7);
  P  = MM(8);
  
  delta=50;
  gamma=75;
  K1=10^-4;
  K2=5*10^-4;
  K3=10^-3;
  K4=5*10^-3;
  K5=10^-2;
  K6=5*10^-2;
  Ko=0.1;
  n=6;
  Oa=10;
  Pa=100;
  mu_1=10^-3;
  mu_2=10^-3;
  mu_3=10^-3;
  mu_4=10^-3;
  mu_5=10^-3;
  mu_6=10^-3;
  mu_o=10^-4;
  mu_p= 10^-5;
  
  CM1= zeros(1,8);
  CM1(1) = (delta*M1*(1-(M1/gamma))-2*K1*M1*M1-M1*sum(i)-((Oa-n)*K3*M1*M3)-((Pa-Oa)*Ko*M1*O)-(mu_1*M1));
  CM1(2) = (K1*M1*M1)-(K2*M1*M2)-(mu_2*M2);
  CM1(3) = (K2*M1*M2)-(K3*M1*M3)-(mu_3*M3);
  CM1(4) = (K3*M1*M3)-(K4*M1*M4)-(mu_4*M4);
  CM1(5) = (K4*M1*M4)-(K5*M1*M5)-(mu_5*M5);
  CM1(6) = (K5*M1*M5)-(K6*M1*M6)-(mu_6*M6);
  CM1(7) = (K6*M1*M6)-(Ko*M1*O)-(mu_o*O);
  CM1(8) = (Ko*M1*O)-(mu_p*P);
end

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Answer 1

Torsten on 14 Jul 2023

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https://uk.mathworks.com/matlabcentral/answers/1996088-how-can-i-input-sum-over-in-function-depend-on-time#answer_1273228

Open in MATLAB Online

Never make changes in the RK4 function. Changes have to be made in the call to RK4 and in f.

tstart = 0;

tend = 100;

dt = 0.01;

T = (tstart:dt:tend).';

Y0 = [10 0 0 0 0 0 0 0];

f = @myode;

Y = fRK4(f,T,Y0);

M1 = Y(:,1);

M2 = Y(:,2);

M3 = Y(:,3);

M4 = Y(:,4);

M5 = Y(:,5);

M6 = Y(:,6);

O = Y(:,7);

P = Y(:,8);

figure

%subplot(3,1,1)

%hold on

plot(T,M1,'r','Linewidth',2)

xlabel('Times (days)')

ylabel('M1 (gr/ml)')

figure

%subplot(3,1,2)

%hold on

plot(T,M2,'b','Linewidth',2)

xlabel('Times (days)')

ylabel('M2 (gr/ml)')

figure

%subplot(3,1,3)

%hold on

plot(T,M3,'g','Linewidth',2)

xlabel('Times (days)')

ylabel('M3 (gr/ml)')

figure

%subplot(3,1,3)

%hold on

plot(T,M4,'b--','Linewidth',2)

xlabel('Times (days)')

ylabel('M4 (gr/ml)')

figure

%subplot(3,1,3)

%hold on

plot(T,M5,'r--','Linewidth',2)

xlabel('Times (days)')

ylabel('M5 (gr/ml)')

figure

%subplot(3,1,3)

%hold on

plot(T,M6,'g--','Linewidth',2)

xlabel('times (days)')

ylabel('M6 (gr/ml)')

figure

%subplot(2,1,1)

%hold on

plot(T,O,'k','Linewidth',2)

xlabel('Times (days)')

ylabel('O (gr/ml)')

figure

%subplot(2,1,2)

%hold on

plot(T,P,'m','Linewidth',2)

xlabel('Times (days)')

ylabel('P (gr/ml)')

function Y = fRK4(f,T,Y0)

N = numel(T);

n = numel(Y0);

Y = zeros(N,n);

Y(1,:) = Y0;

for j = 2:N

t = T(j-1);

y = Y(j-1,:);

h = T(j) - T(j-1);

k0 = f(t,y);

k1 = f(t+0.5*h,y+k0*0.5*h);

k2 = f(t+0.5*h,y+k1*0.5*h);

k3 = f(t+h,y+k2*h);

Y(j,:) = y + h/6*(k0+2*k1+2*k2+k3);

end

function CM1 = myode (~,MM)

M1 = MM(1);

M2 = MM(2);

M3 = MM(3);

M4 = MM(4);

M5 = MM(5);

M6 = MM(6);

O = MM(7);

P = MM(8);

delta=50;

gamma=75;

K1=10^-4;

K2=5*10^-4;

K3=10^-3;

K4=5*10^-3;

K5=10^-2;

K6=5*10^-2;

Ko=0.1;

n=6;

Oa=10;

Pa=100;

mu_1=10^-3;

mu_2=10^-3;

mu_3=10^-3;

mu_4=10^-3;

mu_5=10^-3;

mu_6=10^-3;

mu_o=10^-4;

mu_p= 10^-5;

sumterm = K2*M2 + K3*M3 + K4*M4 + K5*M5;

CM1= zeros(1,8);

CM1(1) = (delta*M1*(1-(M1/gamma))-2*K1*M1*M1-M1*sumterm-((Oa-n)*K3*M1*M3)-((Pa-Oa)*Ko*M1*O)-(mu_1*M1));

CM1(2) = (K1*M1*M1)-(K2*M1*M2)-(mu_2*M2);

CM1(3) = (K2*M1*M2)-(K3*M1*M3)-(mu_3*M3);

CM1(4) = (K3*M1*M3)-(K4*M1*M4)-(mu_4*M4);

CM1(5) = (K4*M1*M4)-(K5*M1*M5)-(mu_5*M5);

CM1(6) = (K5*M1*M5)-(K6*M1*M6)-(mu_6*M6);

CM1(7) = (K6*M1*M6)-(Ko*M1*O)-(mu_o*O);

CM1(8) = (Ko*M1*O)-(mu_p*P);

end

2 Comments
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cindyawati cindyawati on 14 Jul 2023

Edited: cindyawati cindyawati on 14 Jul 2023

is M1 until P depend on time, right?

Torsten on 14 Jul 2023

Edited: Torsten on 14 Jul 2023

It's obvious from your plots, isn't it ?

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How can I input sum over in function depend on time?

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How can I input sum over in function depend on time?

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Accepted Answer

2 Comments Show NoneHide None

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