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I am having trouble solving this set of simultaneous nonlinear equations to determine the unknown variables a,b,c,d,e.

It seems like my code enters in an infinite loop and never stops.

syms a b c d e;
K1=zeros(1,5);
K2=zeros(1,5);
K3=zeros(1,5);
K4=zeros(1,5);
K5=zeros(1,5);

for i=1:9
    x1=[0.5096 0.5092 0.5087 0.4852 0.4847 0.4834 0.4804 0.4805 0.4803];
    x2=[0.0963 0.0964 0.0965 0.1163 0.1161 0.1158 0.1275 0.1266 0.1253];
    x3=[0.3941 0.3944 0.3948 0.3985 0.3992 0.4008 0.3921 0.3929 0.3943];   
    
    T=[394.15 399.15 404.15 375.15 390.15 405.15 374.15 392.15 406.15]; 
    
    K1(i)=exp((-8.549)+(6692/T(i)))
    K2(i)=100
    K3(i)=exp((16.93565)+((1250)/T(i))+(-2.575*log(T(i))))
    K4(i)=exp((-936.28)+((40216.27)/T(i))+(151.983*(log(T(i))))+(-0.1675*(T(i))))
    K5(i)=exp((1044.78)+(-45171.42/T(i))+(-165.20*log(T(i)))+(0.1511*(T(i))))
    
    eqns=[((d*(c-e))/((x1(i)-a-b-c-d)^5)*(x2(i)-d-b-c))==K1(i),...
       ((a+b+c)*a)/((x1(i)-a-b-c-d)^2)==K2(i),...
       ((a+b+c)*(d+b))/((x1(i)-a-b-c-d)*(x2(i)-d-b-c-e))==K3(i),...
       ((a+b+c)*(c-e))/((x1(i)-a-b-c-d)^4*(x2(i)-d-b-c-e))==K4(i),...
       (((e)*(x1(i)-a-b-c-d)^3)/((c-e)*(x3(i)-e)))==K5(i)];

    S=solve(eqns,[a,b,c,d,e]);
    S.a(S.a<0)=[];
    S.b(S.b<0)=[];
    S.c(S.c<0)=[];
    S.d(S.d<0)=[];
    S.e(S.e<0)=[];
    S.a=double(S.a)
    S.b=double(S.b)
    S.c=double(S.c)
    S.d=double(S.d)
    S.e=double(S.e)
end
juju89
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GAGANDEEP KAUR
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1 Answers1

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The issue is not the for loop but the line

S=solve(eqns,[a,b,c,d,e]);

which takes too long to solve the equations.

This could be due to:

  1. The system of equations being too complex and Matlab's symbolic toolbox cannot handle it.
  2. Your system of equations does not have an analytical solution, so you should first consider trying to solve the equations numerically using one of Matlab's ODE solvers, such as ode45.
juju89
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  • Thank you for your response. Actually I am quite beginner to MATLAB so as much as I know ODEs are used for differential equations. If it is still possible may you please advice about its formation and initial guess etc. as I need to evaluate unknown variables rather than 'x' – GAGANDEEP KAUR Nov 04 '20 at 06:10