How I can give condition & plot the solution of this differential equation. . . . . . . Please Guide

1 次查看（过去 30 天）

显示更早的评论

DEEPAK KARARWAL 2022-7-19

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1763810-how-i-can-give-condition-plot-the-solution-of-this-differential-equation-please-guid

回答： MOSLI KARIM 2023-2-16

在 MATLAB Online 中打开

This is the equation for which

boundery condition are

theta(z=0)=0 degree

theta(z=h)=90 degree

where h=6

z=0:h

how to give condition here

e=8.85*10^-12
dele=11
E=1
k11=9
k33=9
k22=11
syms theta(z) z dtheta
dtheta=diff(theta,z)
d2theta=diff(theta,z,2)
eqn=d2theta+((k33-k11)*cos(theta)*sin(theta))*(dtheta)^2*(1/(k11*(cos(theta))^2+k22*(sin(theta))^2))+e*dele*E^2*cos(theta)*sin(theta)*(1/(k11*(cos(theta))^2+k22*(sin(theta))^2))
cond(theta(0)==0, theta(pi/2)==0)
thetaSol = dsolve(eqn,cond)
thetaSol = unique(simplify(thetaSol))
fplot(thetaSol)

7 个评论
显示 5更早的评论隐藏 5更早的评论

Sam Chak 2022-7-22

What is the value of epsilnot? @DEEPAK KARARWAL

DEEPAK KARARWAL 2022-7-22

value of epsilnot=8.85*10^-12

请先登录，再进行评论。

请先登录，再回答此问题。

回答（3 个）

Torsten 2022-7-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1763810-how-i-can-give-condition-plot-the-solution-of-this-differential-equation-please-guid#answer_1012945

编辑：Torsten 2022-7-22

在 MATLAB Online 中打开

dsolve doesn't succeed. Thus use a numerical solver (bvp4c) to solve your equation.

syms A theta(z)

dtheta=diff(theta,z)

dtheta(z) =

d2theta=diff(theta,z,2)

d2theta(z) =

eqn = d2theta + A/2*sin(2*theta)==0;

cond = [theta(0)==0, theta(6)==pi/2];

thetaSol = dsolve(eqn,cond)

Warning: Unable to find symbolic solution.

thetaSol = [ empty sym ]

yes sir, but what I want, is to give such a boundery condition at theta(z)=(__) such that I will get varying angle from 0 to 90 degree as we increase the value of E, where E is electric field and contained in the expression of A.

Torsten 2022-7-28

Not clear what you mean.

The boundary value for theta at z = 6 can be set by writing it in the variable "bv" of my code above. Experiment with it.

请先登录，再进行评论。

Sam Chak 2022-7-22

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1763810-how-i-can-give-condition-plot-the-solution-of-this-differential-equation-please-guid#answer_1013135

在 MATLAB Online 中打开

Hi @DEEPAK KARARWAL

Giiven the parameters, it seems that if you select initial values

and

, the boundary values are satisfied.

epsilnot = 8.85*10^-12;

dele = 11;

E = 1;

k11 = 9;

k33 = 9;

k22 = 11;

A = sqrt(dele*epsilnot*E^2/k11);

f = @(t, x) [x(2); ...

- (A/2)*sin(2*x(1))];

tspan = [0 6];

initc = [0 pi/12]; % initial condition

[t, x] = ode45(f, tspan, initc);

plot(t, x(:,1), 'linewidth', 1.5), grid on, xlabel('t'), ylabel('\theta')

x(end,1) % π/2 at θ(6)

ans = 1.5708

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

DEEPAK KARARWAL 2022-7-22

Thanks you sir , I will analyze it and than report you again, Thank you

请先登录，再进行评论。

MOSLI KARIM 2023-2-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1763810-how-i-can-give-condition-plot-the-solution-of-this-differential-equation-please-guid#answer_1172780

在 MATLAB Online 中打开

 %%
function answer 
clc
clear all
close all
global A 
epsilnot = 8.85*10^-12;
dele     = 11;
E        = 1;
k11      = 9;
k33      = 9;
k22      = 11;
A        = sqrt(dele*epsilnot*E^2/k11);
solinit=bvpinit(linspace(0,6),[0;pi/12])
sol=bvp4c(@fct,@bc,solinit)
figure(1)
plot(sol.x,sol.y(1,:))
    function  dxdy=fct(x,y)
    dxdy=[y(2); -(A/2)*sin(2*y(1))];   
    end 
    function res=bc(ya,yb)
        
    res=[ya(1);yb(1)-90]    
    end 
end 