MATLAB: System of equations (solve exponentiel equations

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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

Best Answer

@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.
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