How to solve a non-linear equation where each element of the array is a parameterized function?
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Dear all,
I need to solve an equation with the following form:
[f(a,b,c); g(a,b,c); p(a,b,c)] = [0; 0; q(t)]
Ok, it's more like
[f(a,b,c,da,db,dc,d2a,d2b,d2c); g(a,b,c,da, db,dc,d2a,d2b,d2c); p(a,b,c,da,db,dc,d2a,d2b,d2c);] = [0; 0; q(t)]
(where "da" means "da/dt" and "d2a" means "d2a/dt2", got using fulldiff())
Or, exactly:
A=
12*d2Gama*cos(Alpha)*cos(Gama)^2 - (9*d2Beta*cos(Gama))/10 - (9*d2Alpha*cos(Beta)*sin(Gama))/10 - 12*d2Gama*cos(Alpha) + 12*d2Gama*cos(Beta)*cos(Gama)^2 - (9*dAlpha^2*cos(Beta)*cos(Gama)*sin(Beta))/10 - 12*dGama^2*cos(Alpha)*cos(Gama)*sin(Gama) - 12*dGama^2*cos(Beta)*cos(Gama)*sin(Gama) + 12*dGama^2*cos(Gama)^2*sin(Alpha)*sin(Beta) + (9*dAlpha*dBeta*sin(Beta)*sin(Gama))/5 + 12*d2Gama*cos(Gama)*sin(Alpha)*sin(Beta)*sin(Gama); (9*d2Alpha*cos(Beta)*cos(Gama))/10 - 12*dGama^2*cos(Beta) - (9*d2Beta*sin(Gama))/10 + 12*d2Gama*sin(Alpha)*sin(Beta) + 12*dGama^2*cos(Alpha)*cos(Gama)^2 + 12*dGama^2*cos(Beta)*cos(Gama)^2 - 12*d2Gama*cos(Gama)^2*sin(Alpha)*sin(Beta) - (9*dAlpha^2*cos(Beta)*sin(Beta)*sin(Gama))/10 - (9*dAlpha*dBeta*cos(Gama)*sin(Beta))/5 + 12*d2Gama*cos(Alpha)*cos(Gama)*sin(Gama) + 12*d2Gama*cos(Beta)*cos(Gama)*sin(Gama) + 12*dGama^2*cos(Gama)*sin(Alpha)*sin(Beta)*sin(Gama); 12*dGama^2*sin(Beta)*sin(Gama) - (9*dBeta^2)/10 - 12*d2Gama*cos(Gama)*sin(Beta) - (9*dAlpha^2*cos(Beta)^2)/10 + 12*dGama^2*cos(Beta)*cos(Gama)*sin(Alpha) + 12*d2Gama*cos(Beta)*sin(Alpha)*sin(Gama)];
B= [0 0 log(t+1)+sin(t)./(t+1)].';
fsolve(A-B)
but let's try to learn the simplest first.
I need to get expressions for a(t), b(t) and c(t).
I believe there's no exact solution, so, it could be an approximated solution, since it returns expressions Alpha(t), Beta(t) and Gama(t).
How do we do Matlab solve it?
Thanks, very much
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回答(2 个)
Torsten
2015-6-19
Add the equations
dalpha/dt=alphadot
dbeta/dt=betadot
dgamma/dt=gammadot,
to your system, substitute
dalpha by alphadot
dbeta by betadot
dGama by gammadot
d2alpha by dalphadot/dt
d2beta by dbetadot/dt
d2Gama by dgammadot/dt
in your equations and use ODE15i to solve.
Best wishes
Torsten.
Marlon Saveri Silva
2015-6-19
1 个评论
Torsten
2015-6-22
I already included the way how to deal with 2nd order derivatives in my reply .
If you have the equation
f(t,y,y',y'')=0,
replace it by the two equations
y'-y1=0;
f(t,y,y1,y1')=0
Best wishes
Torsten.
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