How can i write the eq. in attached file in matlab ? please help.....

this equation is obtained by finite-difference scheme method.

[Walter Roberson]

There is no summation in that equation.

There is also no boundary condition, so the values cannot be computed numerically.

[Prince]

how to write this equation in matlab to compute it numerically ???

[Walter Roberson]

You need boundary conditions. The form of the boundary conditions will give me more information about how to approach it.

[Prince]

A two-point boundary can be posed the orientation director versus the z-coordinate, and it’s controlled by the equation. Dirichlet type used the two boundary conditions for strong anchoring:- θ(z=0)=90 , θ(z=L)=90 where: L =0.2

Answer 1

[Walter Roberson]

Based upon the information you have given, the equation is

theta(k,i) = 0

for all k and i.

[Prince]

sorry i made a mistake ,A two-point boundary can be posed the orientation director versus the z-coordinate, and it’s controlled by the equation. Dirichlet type used the two boundary conditions for strong anchoring:- θ(z=0)=90 , θ(z=L)=90 where: L =0.2

[Walter Roberson]

In email, you asked for the expression anyhow, saying that you will find a way to make the rest work. The expression is

theta(k+1, i) = (1/3) * (-(theta(k, i+1) + theta(k, i) + theta(k, i-1)) + 1/6*(V^2/Vth^2)*pi^2*h^2*sin(2*theta(k, i)))

However, if Vth is intended as having a relationship to V then this might need to change a bit.

The validity of the expression depends upon how the boundary conditions are expressed, whether they start from theta(k,0) or from theta(k,1) or theta(k,2); the expression would also need to change if the first k was 0 instead of 1.

You expressed a boundary condition on theta(z=0) without giving any way to interpret that in terms of theta(k,i) . If we guess that maybe you want to start numbering i from 0, then we run into the problem that your other boundary condition is theta(z=0.2) and certainly 0.2 is not a valid array index. Is the idea that you divided the length L up into pieces indexed at i? Or indexed at k? We do not know, but you are going to have to know if you want to make use of the expression you asked for.

[Prince]

thanks a lot