Solve a large composite set of equations numerically
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I have the following set of equations:
1:
where are known scalar constants, and
2:
3:
where Vis known scalar constant and k is a scalar which I want to find.
4:
5:
I've been informed to find the value of k from the last following two inequalities:
with
and are known constants.
Just to make things little more easier, let
The ultimate problem here is that do not have explicit symbolic equations because I have to compute them numerically since their direct symbolic equations are too complicated and Matlab symbolic engine produces too big output.
So the question is: how to numerically solve inequalities (5:) for the variable k ?
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darova
2020-1-14
I think there is no exact solution for k. Try something like this:
% 1
[X,Y,Z] = ndgrid( linspace(-1e5,1e5,20) );
f = fx*X + fy*Y + fz*Z + d1;
% 2
r = sqrt(f.^2+g.^2);
% 3
k = 2; % assume
vzd = -V*(f*fz+g*gz).*tanh(k*r)./Nc + ...
% 4
gammad = atand2(vzd,vxd);
delta = 2e5/20;
[Bx,By,Bz] = gradient(gammad,delta);
% 5
F1 = sqrt(Bx.^2+Bz.^2) - 7*(1-alpha)*gamma_max/10/V;
F2 = By - alpha*gamma_max/V;
isosurface(X,Y,Z,F1,0)
hold on
isosurface(X,Y,Z,F2,0)
hold off
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