Solving Non-Linear Equation in a loop

I want to solve this equation for different values of E0, I want to vary the value of E0 from 1 to 100, for which I will get 99x3 equations+1 as E0 is present in 3 out of 4 equations given below. I can solve the equation for a fix value of E0 using VPA solve but I can't write a program to iterate the value of E0 for which I should get 99 different values of E,P,F and S from the equation for 99 different values of E0.

clc;clear;close;

syms E F S P

E00=1; %Total concetration of E0

F0=100; %TotalCOncentration of F0

k1=4; %rate constants

k2=6;

k3=4;

k4=1;

k5=6;

k6=4;

k7=5;

k8=8;

for i=1:99

E0(i)=E00+i;

eqn1=(E0-E)*(k1+k2)-k1*E*S-k4*E*P==0; % First equation

eqn2=(E0-E)*k3+(F0-F)*k6-E*S*k1-k8*S*F==0; %Second equation

eqn3=(F0-F)*(k7+k6)-F*P*k5-k8*S*F==0; %Third equation

eqn4=k2*(E0-E)+(F0-F)*k7-k5*F*P-k4*E*P==0; %Fourth Equation

sol(i)=solve([eqn1,eqn2,eqn3,eqn4,E>0,S>0,P>0,F>0,E<100,F<100,S<100,P<100],[E,P,S,F]);

end

heres my second code for a single value of E0

clc;clear;close;

%% Initial conditons and values of rate constants

syms E S F P

E0=1; %Total concetration of E0

F0=100; %TotalCOncentration of F0

k1=4; %rate constants

k2=6;

k3=4;

k4=1;

k5=6;

k6=4;

k7=5;

k8=8;

%% The equations

eqn1=(E0-E)*(k1+k2)-k1*E*S-k4*E*P==0; % First equation

eqn2=(E0-E)*k3+(F0-F)*k6-E*S*k1-k8*S*F==0; %Second equation

eqn3=(F0-F)*(k7+k6)-F*P*k5-k8*S*F==0; %Third equation

eqn4=k2*(E0-E)+(F0-F)*k7-k5*F*P-k4*E*P==0; %Fourth Equation

equations=[eqn1 eqn2 eqn3 eqn4]; %Total equations

vars=[ E S P F];

range=[0 E0-0.1;0.1 E0-0.1;0.1 E0-0.1;0.1 F0-0.1]; %Range of variables to omit unwanted values

% Range has been taken from 0 to E0-0.1 so that the value of E does not

% exceed the value of E0, same is done for S P and F

%% Solver

sol=vpasolve(equations,vars,range);

[sol.E sol.S sol.F sol.P];

%% Values

E=sol.E %Numerical value of E

P=sol.P %Numerical value of P

S=sol.S %Numerical value of S

F=sol.F %Mumerical value of F

digits(4);

x=P/(P+S)

b=E0/F0; %E0/F0

I just can't write a code for E0=1 to 99, I tried to put vpa into loop, but it doesn't work. Please help me out

Answer 1

[Mahesh Taparia]

Hi

The function vpasolve returns the structure which can be stored in a cell array. Also there were some missing initialization. The below code will work for your problem:

clc;clear;close;
syms E F S P
E00=1;                    %Total concetration of E0
F0=100;                  %TotalCOncentration of F0
k1=4;                    %rate constants
k2=6;
k3=4;
k4=1;
k5=6;
k6=4;
k7=5;
k8=8;
E0=zeros(100,1);
sol=cell(100,1);

for i=1:99
    E0(i)=E00+i;
    eqn1=(E0(i)-E)*(k1+k2)-k1*E*S-k4*E*P==0;           % First equation
    eqn2=(E0(i)-E)*k3+(F0-F)*k6-E*S*k1-k8*S*F==0;      %Second equation
    eqn3=(F0-F)*(k7+k6)-F*P*k5-k8*S*F==0;           %Third equation
    eqn4=k2*(E0(i)-E)+(F0-F)*k7-k5*F*P-k4*E*P==0;      %Fourth Equation
    
    
    equations=[eqn1 eqn2 eqn3 eqn4];                       %Total equations
vars=[ E S P F];                                  
range=[0 E0(i)-0.1;0.1 E0(i)-0.1;0.1 E0(i)-0.1;0.1 F0-0.1];   %Range of variables to omit unwanted values

sol{i}=vpasolve(equations,vars,range);
end

Hope it will help!

[Alakesh Upadhyaya]

Thank you, thats helpful.