Solve issue in Matlab R2018b

I was using Matlab R2014a earlier where I was able to solve this equation easily, but in Matlab R2018b it is returning the

error in sol = solve(eqn,a,[0 pi]); I couldn't figure out why. The working code in Matlab 2014a is

syms a T
v2=-2.3750
g=1;
b=0;
e2=0.5;
k=2.5;
w=-2*cos(k);
eqn = sin(3*k+a)./sin(2*k+a)==v2-w+(g.*T.^2)+(e2.*T.^2.*sin(k)^2)./(sin(2*k+a)^2+b*T.^2*sin(k).^2);
sol = solve(eqn,a,[0 pi]);
digits(5)
solutions = vpa(subs(sol),3)

Please note that "a" is to be bound to take values between 0 and pi.

[Image Analyst]

What is the exact error (ALL the red text)? Have you tried it with R2019a?

[madhan ravi]

Only you can specify the range in vpasolve() where only one parameter is not known but with solve you can't specify the bounds.

[John Jarvis]

@Image Analyst:

The exact errors are as follows (all the red text)

Error in solve>getEqns (line 429)

[eqns, vars] = sym.getEqnsVars(argv{:});

Error in solve (line 226)

[eqns,vars,options] = getEqns(varargin{:});

Error in SolutionsPlot (line 11)

sol = solve(eqn,a,[0 pi]);

Answer 1

[Star Strider]

Restrict ‘a’ using an assume call.

Try this:

syms a T
assume(a >= 0 & a <= pi)
v2=-2.3750
g=1;
b=0;
e2=0.5;
k=2.5;
w=-2*cos(k);
eqn = sin(3*k+a)./sin(2*k+a)==v2-w+(g.*T.^2)+(e2.*T.^2.*sin(k)^2)./(sin(2*k+a)^2+b*T.^2*sin(k).^2);
[sol,prms,conds] = solve(eqn,a, 'ReturnConditions',true)
digits(5)
solutions = vpa(subs(sol),3)
vpaconds = vpa(conds)

[John Jarvis]

@Star Strider Thanks. Is there a way that I can get those nice numeric solutions which I used to get with the same code in R2014a? These conditions make it hard to explicityly see the numerical solutions.

[Star Strider]

My pleasure.

The ‘conds’ result is likely as good as it gets. Note that it is a function of ‘T’, and with the inequality conditions stated in the vector, neither coeffs or any related function (such as numden or sym2poly) will produce a purely numeric result.

Adding:

Tsol(:,1) = solve(conds(1), T)
Tsol(:,2) = solve(conds(2), T)

doesn’t completely resolve the problem, since the result is now a funciton of ‘x’:

Tsol =
 -2*exp(-5i/4)*(-((exp(x*2i)*exp(10i) - 1)*(4478027322974943*exp(5i/2) - 1125899906842624*exp(x*2i)*exp(15i) - 4478027322974943*exp(x*2i)*exp(25i/2) + 1125899906842624))/(4503599627370496 + 4503599627370496*exp(x*4i)*exp(20i) - 12233297969360201*exp(x*2i)*exp(10i)))^(1/2)
  2*exp(-5i/4)*(-((exp(x*2i)*exp(10i) - 1)*(4478027322974943*exp(5i/2) - 1125899906842624*exp(x*2i)*exp(15i) - 4478027322974943*exp(x*2i)*exp(25i/2) + 1125899906842624))/(4503599627370496 + 4503599627370496*exp(x*4i)*exp(20i) - 12233297969360201*exp(x*2i)*exp(10i)))^(1/2)

The only other option I can provide is:

  Tfcn = matlabFunction(Tsol)

that will produce an anonymous function to evaluate those.

[John Jarvis]

@Star Strider, Many thanks for your elaboration.

[Star Strider]

As always, my pleasure.