how to solve this equation in matlab? Please help

please help me for solving this equation in matlab , thank you all , see the attached file.

Answer 1

[Torsten]

Use MATLAB's bvp4c to solve

y1' = y2
y2' = a*sin(y1)*cos(y1)

(a=V^2/V_th^2*Pi^2/L^2)

with boundary conditions

y1(0.01)=Pi/2
y1(L)=Pi/2

Best wishes

Torsten.

[Prince]

would you please write the full codes for this ?

[Torsten]

function main
L=...;
a=...;
solinit = bvpinit(linspace(0,L,10),@init);
sol=bvp4c(@(x,y)ode(x,y,a),@bc,solinit);

function dydx=ode(x,y,a)
dydx=[y(2);a*sin(y(1))*cos(y(1))];

function res=bc(ya,yb)
res=[ya(1)-pi/2;yb(1)-pi/2];

function ic=init(x)
ic=[pi/2;0];

Best wishes

Torsten.

[Prince]

Thanks a lot

[Prince]

Hi , can you please check the mfile i have attached it for the this equation?, and also how can i plot the equation? thanks a lot for your kind help.

[Torsten]

To plot, add

x = linspace(0,L,20);
y = deval(sol,x);
plot(x,y(1,:));

after the line

sol=bvp4c(@(x,y)ode(x,y,a),@bc,solinit);

Best wishes

Torsten.

Answer 2

[Explorer]

L =0.2;
K11 =4.8e-12;
E0 =8.85e-12;
delta_E =0.78;

Vth = (pi/L) * sqrt(K11/(E0*delta_E))

[Prince]

thanks a lot