Equations which depend on each other with unknown initial value
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Hi all,
I want to solve equations which depend on each other such as,
5*x_1 = 3*x_2 + 4
4*x_2 = 2*x_1 + 4*x_3 + 4
4*x_3 = 2*x_2 + 4*x_4 + 4
3*x_4 = 6*x_3 +4
I usually put the coefficients of the variables into matrix
A = [5 -3 0 0; -2 4 -4 0; 0 -2 4 4; 0 0 -6 3]
C = [4;4;4;4]
B = inv(A) * C
and get the result, since the number of variables can change and go up to 100, I wrote a 'for loop'
n=4;
for i = 2:n-1
x(1) = (3*x(2) + 4)/5
x(i) = (2 * x(i-1) + 4 *x(i+1) +4)/4
x(n) = (3 * x(i-1) + 4) / 3
end
but the results are not same, i think in the for loop matlab assumes x(2) as zero and continues, anyway if someone can solve this problem I appreciate.
Thanks.
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Answers (1)
Walter Roberson
on 5 Nov 2019
n=4;
x = sym('x', [1 n]);
x(1) = (3*x(2) + 4)/5;
for i = 2:n-1
x(i) = (2 * x(i-1) + 4 *x(i+1) +4)/4;
end
x(n) = (3 * x(i-1) + 4) / 3;
4 Comments
Walter Roberson
on 6 Nov 2019
You should go through the equations and make sure that they are correct.
Note: when you construct equations in symbolic form, it is not necessary to do the division by 4 and whatever. You can code things like 5*x(1) == 4*x(2) + 4 inside the eq vector.
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