# how to solve this bvp4c?

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NURUL AISYAH JOHAN on 5 Jan 2020
Commented: darova on 25 Feb 2020
Hello, can anyone help me solve this bvp4c program?
as to solve this problem, I already try numerous initial numbers.
it's either
Unable to solve the collocation equations -- a singular Jacobian encountered.
or
Warning: Unable to meet the tolerance without using more than 1250 mesh points.
The last mesh of 892 points and the solution are available in the output argument.
The maximum residual is 85.3834, while requested accuracy is 1e-07.
here is the bvp4c:
format long g
global alpha beta phi phid epsilon delta rhoS rhoF Y betaT Ec cpS cpF kf knf Pr Tv A B w Q ks
a=0; b=15;
phi=0.5;phid=0.2;delta=0.5;A=0.5;B=0.5;w=1.5;
betaT=0.2;alpha=0.5;beta=0.5;Ec=0.2;Y=0.01;Pr=6.2;Tv=0.488;epsilon=0.1;
rhoF=997.1;cpF=4179;kf=0.613;
rhoS=8933;cpS=385;knf=0.81629325;
Q=((ks+(2*kf))-(2*phi*(kf-ks)))/((ks+(2*kf))+(phi*(kf-ks))); ks=400;
solinit = bvpinit(linspace(a,b,100),@fluidparticle_init);
options = bvpset('stat','on','RelTol',1e-7);
sol = bvp4c(@fluidparticle_ode,@fluidparticle_bc,solinit,options);
sol.y(3,1)
sol.y(7,1)
plot(sol.x,sol.y(2,:),':r')
function dydx=fluidparticle_ode(x,y,alpha,beta,phi,phid,Y,betaT,Ec,kf,knf,Pr,Tv,A,B,rhoS,rhoF,cpS,cpF,Q)
global alpha beta phi phid Y betaT Ec kf knf Pr Tv A B rhoS rhoF cpS cpF Q
dydx=[y(2);
y(3);
(((1-phi)^2.5)*(1-phi+(phi*(rhoS/rhoF)))*((y(2)^2)-(y(1)*y(3))))-((((1-phi)^2.5)/(1-phid))*alpha*beta*(y(5)-y(2)));
y(5);
((y(5)^2)-(beta*(y(5)-y(2))))/y(4);
y(7);
(1-phi+(phi*((rhoS*cpS)/(rhoF*cpF))))*(Pr/Q)*((2*y(2)*y(6))-(y(1)*y(7)))-((Pr/Q)*((alpha*betaT*(y(8)-y(6)))-((alpha*Ec/Tv)*((y(5)-y(2))^2))))
((2*y(5)*y(8))+(Y*betaT*(y(8)-y(6))))/y(4)];
function res=fluidparticle_bc(ya,yb,epsilon,delta,w)
global epsilon delta w
res=[ya(2)-epsilon-(delta*ya(3))
ya(1)
yb(2)
yb(5)
yb(4)-yb(1)
ya(6)-1-(w*ya(7))
yb(6)
yb(8)];
function v=fluidparticle_init(x)
v=[0.5
-exp(-x)
exp(-x)
0.3
-0.5
-exp(-x)
exp(-x)
-exp(-x)];
what should I adjust in this program?

darova on 5 Jan 2020
NURUL AISYAH JOHAN on 6 Jan 2020
〖(1-ϕ_d)/(1-ϕ)^2.5〗f^''' - (1-ϕ_d) [1-ϕ+ϕ(ρ_s/ρ_f )](f^'2-〖ff〗^'' )+αβ(F^'- f^' )= 0.....(1)
F^'2-FF^''-β(f^'-F^' )=0.....(2)
(1/Pr)(k_nf/k_f ) θ^''-(1-ϕ+ϕ((ρC_p )_(s )/(ρC_p )_f ))(2f^' θ- fθ^' )+ αβ_T (θ_p-θ)+αEc/τ_v (F^'-f^' )^2 = 0.....(3)
2F^' θ_p-Fθ_p^'+γβ_T (θ_p-θ)=0.....(4)
Boundary condition:
f^' (0) = ε+δf^'' (0), f(0) = 0, θ(0) = 1+ωθ'(0)
f^' (η)=0, F^' (η)=0, F(η)=f(η), θ(η)=0, θ_p (η)=0 as η → ∞

darova on 6 Jan 2020
I re-wrote the main equations (compare yours and mine) and tried b = 1
Check the attachment

Show 1 older comment
darova on 9 Jan 2020
• Why the limit is only at b=1?
I tried b=2 and this is what i got
NURUL AISYAH JOHAN on 25 Feb 2020
thank you so much for your help. you have help me big time.
but, i have new question about this matter. Why I get error when apply negative value for epsilon?
when epsilon=-0.5, the result:
Error using bvp4c (line 251)
Unable to solve the collocation equations -- a singular Jacobian encountered.
Error in f (line 26)
sol = bvp4c(@fluidparticle_ode,@fluidparticle_bc,solinit,options);
darova on 25 Feb 2020
It's hard to say without knowing of the equations. What is the meaning of epsilon? Maybe it can't be negative?