Numerical solution to a larger equation.

Hi!

I have a very large and complicated equation:

sinh(5.9605e-08*(((1.1259e+15*lamda2^2 + 7.5126e+15)^2)^(1/2) + 7.5126e+15)^(1/2))*sin(2*lamda2)*(lamda2^2 + 8.8818e-16*((1.1259e+15*lamda2^2 + 7.5126e+15)^2)^(1/2) + 6.6725)=0

I need to solve for lamda2. Matlab is unable to solve this. I am getting only 0 as answer. It should not be zero.

Any help will be appreciated.

[Dyuman Joshi]

"Matlab is unable to solve this."

What makes you think so? How did you try to solve it?

"It should not be zero."

Why not? Zero is a root to the equation.

There are infinite solutions to the equation as mentioned by @Alex Sha below, Which other values do you want as the solution?

Answer 1

[Torsten]

What is the zero of your choice ?

fun = @(lamda2)sinh(5.9605e-08*(((1.1259e+15*lamda2^2 + 7.5126e+15)^2)^(1/2) + 7.5126e+15)^(1/2))*sin(2*lamda2)*(lamda2^2 + 8.8818e-16*((1.1259e+15*lamda2^2 + 7.5126e+15)^2)^(1/2) + 6.6725);
lamda2 = -3.2:0.001:3.2;
flamda2 = arrayfun(@(lamda)fun(lamda),lamda2);
plot(lamda2,flamda2)
grid on

[Alex Sha]

There are infinite solutions (including 0)：Lamda2 = n*pi，where n=[...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...]

[Torsten]

@Alex Sha

You are correct, I missed the sin(2*lamda2) term. So lamda2 = n/2 * pi (n integer) are roots of the function.