Matlab code for 2nd order differential equations

(d^2 u(x))/〖dx〗^2 =(γu(x))/(1+αu(x))

(d^2 v(x))/〖dx〗^2 =y〖∆v〗^* (dv(x))/dx-2/ε (γu(x))/((1+αu(x)))

at x=0,u=1,v=0

at x=1,du/dx=0,dv/dx=0

ε=1,α=0.001,y=20,〖∆v〗^*=0.1,γ=1,2.5,5,10,100

How to write matlab code for 2nd order differentials and plots between u vs x, v vs x

[Walter Roberson]

Do you have access to the Symbolic Toolbox? If you do then I suggest that you read the documentation for odeFunction

[KARUNA BOPPENA]

Yes, Thank you for your response

Answer 1

[Sam Chak]

Hi @KARUNA BOPPENA

Which textbook are you referring to for this problem? This appears to be a boundary value problem.

The solution of interest is to be determined by both the boundary conditions

and the gamma parameter γ.

You can find some examples in this bvp4c() documentation:

https://www.mathworks.com/help/matlab/ref/bvp4c.html

[KARUNA BOPPENA]

Thank you so much for your suggestions