solve() is unable to find a solution

Hello everyone,

I was trying to solve a transcendental eqation in MATLAB

I performed two programs one graphical approach and another by solve()

In the graphical approach, I find one solution exists in the range ∈ () for , as shown in the figure below

i.e., the intersection of blue and red curve ()

Now, when i performed another program (T2.m) using solve() :

Command Prompt is giving empty sym with the following message:

Warning: 3 equations in 1 variables.

> In C:\Program Files\MATLAB\R2013a\toolbox\symbolic\symbolic\symengine.p>symengine at 56

In mupadengine.mupadengine>mupadengine.evalin at 97

In mupadengine.mupadengine>mupadengine.feval at 150

In solve at 170

In T2 at 16

Warning: Explicit solution could not be found.

> In solve at 179

In T2 at 16

k1_sol = [ empty sym ]

My T2.m is as follows:

    clc
    clear all
    close all
    one_eV= 1.6/(10^19);
    Vo=0.3 * one_eV;
    b=5/(10^9);
    S=Vo*b;
    a=10/(10^9);
    m=0.067 * 9.1/(10^31);
    h=6.626/(10^34);
    hbar= h/(2*pi);
    k=pi/(4*a);
    lhs= cos(k*a);
    syms k1
    rhs=cos(k1*a) + (m*S)*sin(k1*a)/(hbar^2 * k1);
    k1_sol= solve(lhs== rhs,k1 >= 0.27*(10^9), k1 <= 0.32*(10^9))

so, how to rectify this?

Answer 1

[Alan Stevens]

Just solve it numerically using fzero. Take the initial guess close to the average value of the bounds you specify:

k1_0 = 0.29E9;   % initial guess
k1 = fzero(@k1fn,k1_0);
disp(k1)
disp(cos(pi/4)) % = cos(k*a)  

function Z = k1fn(k1)
one_eV= 1.6/(10^19);
Vo=0.3 * one_eV;
b=5/(10^9);
S=Vo*b;
a=10/(10^9);
m=0.067 * 9.1/(10^31);
h=6.626/(10^34);
hbar= h/(2*pi);
k=pi/(4*a);

Z = cos(k1*a) + (m*S)*sin(k1*a)/(hbar^2 * k1) - cos(k*a);
end

this reults in

2.7859e+08 for k1 and 0.7071 for left and right hand sides of your equation.

[SOURAV KUMAR]

@Alan Stevens can you please tell me why solve() is not able to find the solution?

[Alan Stevens]

I don't know!