boundary conditions at infinity

Good afternoon one and all. Good afternoon torsten sir

Sir my code is working by taking the boundary conditions as x = linspace(0,1,100) but doesnot working at x = linspace(0,Inf,100);

I request you sir please help me how to write the code for 3 sets of boundary conditions at η ≥0 , η =0 and η→∞.

I attached my equations image and my code error below.

My code :

x = linspace(0,Inf,100);

yinit = [0 1 0 1 0 1 ];

init = bvpinit(x,yinit);

options = bvpset('RelTol',1e-8,'AbsTol',1e-12);

sol = bvp4c(@odefun, @bcfun, init,options);

plot(sol.x, sol.y)

hold on

function dydx = odefun(x,y) % equations being solved

x0=1;x1=1;x2=1;x3=1;x4=1;x5=1;x6=1;s=1;Da=1;Gr=1;Gc=1;prs=1;Ra=1;Qr=1;Sc=1; Kr=1; E=1;n=1;s=1;

us = y(1);

usy = y(2);

theta = y(3);

thetay = y(4);

phi = y(5);

phiy = y(6);

dydx = zeros(6,1);

dydx(1) = usy;

dydx(2) = ((1/x0)*(x1*s*us)+(x0/Da)*us-x2*Gr*theta-x3*Gc*phi-(E/s)*(exp(-s*n)));

dydx(3) = thetay;

dydx(4) = ((1/x5)*(x4*prs*theta)+Ra*theta-Qr*theta);

dydx(5) = phiy;

dydx(6) = (Sc/x6)*(s*phi+Kr*phi);

end

function res = bcfun(yL,yR)

s=1;k=1;

res = zeros(6,1);

res(1) = yL(1)-(1/(2*1i))*(1/(s-1i*k)-1/(s+1i*k));

res(2) = yL(3)-(1/s^2)*(1-exp(-s));

res(3) = yL(5)-(1/s^2)*(1-exp(-s));

res(4)= yR(1);

res(5)= yR(3);

res(6)= yR(5);

end

ERROR:

Error using bvp4c (line 248)

Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in bvpmodel (line 12)

sol = bvp4c(@odefun, @bcfun, init,options);

Answer 1

[Torsten]

You must use a sufficiently large number instead of "Inf" here:

x = linspace(0,Inf,100)

x = 1x100

0 Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf Inf

[mallela ankamma rao]

Thank you very much for your response torsten sir

I understood how did write code for remaining two set of boundary conditions sir

but i couldnot understand the first set of boundary conditions.

Sir i request you please tell me how to write code for

u1=0, θ=0 and φ =0 for η ≥0

(here u1= yL(1), θ=yL(3), φ=yL(5))

[Torsten]

As written, I also don't understand the part u1=0, θ=0 and φ =0 for η ≥0. Maybe you could include the complete description of the problem (e.g. it is referred to (11) which is not part of your graphics).

[mallela ankamma rao]

Good evening sir

Sir actually after applying Laplace transform, the equations and boundary conditions ( refered as (11) ) are changed into equations (12), (13), (14) and boundary conditions changed into (15).

Please look at attached image sir.

At η =0 and η = ∞, we can write code for BCs sir

but for η ≥0, i can not understand how to write code for BCs sir

Please help me to write code for this sir

[Torsten]

As I wrote, I don't understand this either. Maybe including (8) - (11) can shed some light on it.

[mallela ankamma rao]

Good evening sir

I attched the 8 to 11 equations also sir

Please help to write the code sir

[Torsten]

I suggest solving equations (8), (9) and (10) directly using "pdepe".

[mallela ankamma rao]

Thank you sir. i will try in pdepe method