system of equations (solve exponentiel equations

Hi,

I want to solve this system of equations

P= exp(-r.^2.*P+R.^2.*Q).*sum((r.^2.*P +R.^2.*Q).^m./factorial(m)) // with m=(0:1:k-1); ;k=5

Q=exp(-r.^2.*P + R.^2.*Q.*sum((r.^2*P + R.^2.*Q).^n./factorial(n)) // n=(k:1:K_avg); K_avg=10

I tried to solve this system with solve. the result of execution : error eqns.

do you have an idea ?

th = -80:-3:-106;
list1 = zeros(size(th));
list2 = zeros(size(th));
 r=[ 15.8 20.8 27.5 36.3 47.6 63.9 83.1 109.6 115.2];
 R=[ 8.12 10.9 14.4 19.2 25.6 33.1 43.5 75.6 80.2];
for i = 1:numel(th)
K_avg=17;
k=9;
m=(0:1:k-1);
n=(k:1:K_avg);
syms P Q
eqns= [exp(-r.^2.*P+R.^2.*Q).*sum((r.^2.*P +R.^2.*Q).^m./factorial(m))-P==0,exp(-r.^2.*P + R.^2.*Q.*sum((r.^2*P + R.^2.*Q).^n./factorial(n))-Q==0)];
vars = [P Q];
[sol1,sol2]=solve(eqns,vars);
list1(i) = sol1;
list2(i) = sol2;
end

Answer 1

[madhan ravi]

@Marwen you get error/s because the number of elements m,n and R,r are not the same in order to make the loop perform calculations all the arrays should have the same number of elements.

[Marwen Tarhouni]

@madhan ravi, i modified the number of elements of {m,n,R,r}, I get the same error with the number of elements is the same.

[madhan ravi]

upload your modified code

[madhan ravi]

syms P Q

%neglected to loop to check if theres any possible solution to be attained but the solution is an empty sym which means no solution.

th = -80;

   r=[ 15.8];

   R=[ 8.12];

   m=0;

n=(k);

eqn1= exp(-r.*r.*P+R.*R.*Q.*sum((r.*r.*P +R.*R.*Q).*(m.*m)./factorial(m))-P);
eqn2=exp(-r.^2.*P + R.^2.*Q.*sum((r.^2*P + R.^2.*Q).^n./factorial(n))-Q);

K_avg=10;

k=5;

[sol1,sol2]=solve(eqn1,eqn2,[P Q])

Matlab is not able to solve it.

[Marwen Tarhouni]

@ madhan ravi, thank you for your explanation , but when i add lambda*pi in the equation

lambda= 1.0000e-04;
eqn1=exp(lambda*pi*r.^2.*P+lambda*pi*R.^2.*Q).*sum((lambda*pi*r.^2.*P +lambda*pi*R.^2.*Q).^m./factorial(m))-P;
eqn2=exp(-lambda*pi*r.^2.*P + lambda*pi*R.^2.*Q).*sum((lambda*pi*r.^2*P + lambda*pi*R.^2.*Q).^n./factorial(n))-Q;
vars = [P Q];
[sol1. sol2]=solve(eqn1,eqn2,vars);

result:Warning: Cannot solve symbolically. Returning a numeric approximation instead.

[madhan ravi]

Sol=vpasolve(eqn1,eqn2)

[Marwen Tarhouni]

@ madhan ravi :result of execution

Sol = 

    P: [1x1 sym]
    Q: [1x1 sym]
what does this solution mean :empty solution?

[madhan ravi]

Sol.P
Sol.Q

give a vote if you get the answer :)

[Marwen Tarhouni]

@madhan ravi, thank you :problem solved

[madhan ravi]

@Marwen your welcome.