need to find to root of equation
1 view (last 30 days)
Show older comments
Arvind Sharma
on 20 Sep 2020
Answered: Walter Roberson
on 20 Sep 2020
% need to find the value of x for different values of y
y=0.00:0.001:0.08;
dEv=25 meV;
dEvbm=x.*(1.6)+y.*(-0.52);
C=1.05;
V=C.*sqrt(y);
dEv=(((dEvbm-1.0)+sqrt(((dEvbm+1.0).*(dEvbm+1.0))+(4.V.*V)))/2);
% how to find the value of x
0 Comments
Accepted Answer
Walter Roberson
on 20 Sep 2020
syms x y real
syms delta_x delta_y delta_C real
assume(y >= 0);
assume(delta_x >= -5/100 & delta_x < 5/100);
assume(delta_y >= -5/1000 & delta_y < 5/1000);
assume(delta_C >= -5/1000 & delta_C < 5/1000);
dEv = 25;
dEvbm = x.*(16/10 + delta_x) + y.*(-52/100 + delta_y);
C = 105/100 + delta_C;
V = C .* sqrt(y);
eqn = dEv == (((dEvbm - 1) + sqrt(((dEvbm + 1) .* (dEvbm + 1)) + (4 .* V.*V)))/2);
sol = solve(eqn, x, 'returnconditions', true);
sol.x
sol.conditions
Y = 0.00:0.001:0.08;
X = subs(sol.x, y, Y);
disp(X)
You will get answers similar to
-(delta_C^2/26000 + (21*delta_C)/260000 + delta_y/1000 - 260004967/10400000)/(delta_x + 8/5)
Here, delta_C reflects the undercertainty in the value of C: when you write C = 1.05 then in science that stands in for C being a unknown value that is in the range 1045/1000 (inclusive) and 1055/1000 (exclusive.) It makes no sense to ask for exact solutions to equations that have coefficients that are not exactly known, so I have converted to exact solutions by quantifying the uncertainties.
Does it really make a difference? Yes, it does. For X(2), if you examine over the entire range of uncertainties, the results come out between 15.1518013280886 and 16.1293438703474, which is a quite noticable difference.
I assumed here that dEv = 25 was an exact figure, and that the + 1.0 and - 1.0 were intended to be exact 1's and the 4 multiplying the V^2 was intended to be an exact 4 and the division by 2 was intended to be an exact 2.
0 Comments
More Answers (0)
See Also
Categories
Find more on Calculus in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!