Matlab code for boundary condition

What is the matlab code for below the boundary conditon?

(i) x=0, y=0

(ii) x=0, dy/dx +dz/dx =0

(iii) t=0, x=infinity, y=1, z=c

[Torsten]

Depends on the numerical program for which you try to implement these conditions.

[Salai Mathiselvi Salai Mathiselvi]

y''(x,t)-y^2*y'(x,t)+a*z(x,t)-c*y(x,t)-y'(t)=0

z''(x,t)-y^2*z'(x,t)-a*z(x,t)+c*y(x,t)-z'(t)=0

Boundary condition

(i) x=0, y=0

(ii) x=0, dy/dx +dz/dx =0

(iii) t=0, x=infinity, y=1, z=b

What is the matlab code for this equation?

[Torsten]

What is the difference between y'(x,t) and y'(t) ?

Same for z.

According to which independent variable do you differntiate when you write y', y'', z', z'' ?

[Torsten]

Salai Mathiselvi Salai Mathiselvi's comment moved here:

d^2y/dx^2-y^2*dy/dx+a*z-c*y-dy/dt=0,

d^2z/dx^2-y^2*dz/dx+a*z-c*y-dz/dt=0

Boundary condition

(i) x=0, y=0

(ii) x=0, dy/dx +dz/dx =0

(iii) t=0, x=infinity, y=1, z=b

What is the matlab code for this equation?

Answer 1

[Torsten]

So you mean

at x=0, you have y = 0 and dy/dx + dz/dx

at x=infinity, you have y=1 and z = b

and at t = 0, you have

y = 1, z = b

for all x in [0;infinity] ?

If you have numerical values for a, b and c, read the documentation of "pdepe".

It will show you how to write the MATLAB code for your equations.

[Salai Mathiselvi Salai Mathiselvi]

Matlab Program

function pdex4

m = 2;

x = linspace(0,5);

t = linspace(0,1000);

sol = pdepe(m,@pdex4pde,@pdex4ic,@pdex4bc,x, t);

u1 = sol(:, :, 1);

u2 = sol(:, :, 2);

% A solution profile can also be illuminating.

figure

plot(x,u1(end,:))

% A solution profile can also be illuminating.

figure

plot(x,u2(end,:))

%--------------------------------------------------------------------

function [c, f, s] = pdex4pde(x,t,u,DuDx)

c = [1;1];

f = [1;1].*DuDx;

k = 0.1;

k1 =0.5;

F=k*u(2)-k1*u(1);

F1=-k*u(2)+k1*u(1);

s = [F;F1];

%---------------------------------------------------------------------

function u0 = pdex4ic(x)

u0 =[1;1];

%---------------------------------------------------------------------

function [pl, ql, pr,qr] = pdex4bc(xl,ul,xr,ur,t)

pl = [0;ul(1)];

ql = [1;1];

pr = [ur(1)-1;ur(2)];

qr = [1;1];

Is it correct? if not how should i correct this for different values of 't'?

[Torsten]

1. m = 2 is wrong.
2. You didn't include the terms -y^2*dy/dx and -y^2*dz/dx in the equations.
3. Your boundary conditions settings are all wrong.

To include the boundary condition dy/dx + dz/dx = 0 at x=0 for "pdepe", you will have to rewrite your system of equations in terms of y and u:=y+z. This leads to

d^2y/dx^2-y^2*dy/dx+a*(u-y)-c*y-dy/dt=0,
d^2u/dx^2-y^2*du/dx-du/dt = 0

Best wishes

Torsten.

[Salai Mathiselvi Salai Mathiselvi]

Thank you very much sir. Your anwer was very helpful my work.