# Error in quad function-maximum function count exceeded. "Singularity likely" warning when I use the QUADL function in MATLAB

7 views (last 30 days)
FANI on 29 Sep 2014
Commented: FANI on 30 Sep 2014
Hi all, I need help using the quadl function.
clear all close all clc format long gamma=1.4; r=10; n=1000; h =(r)/n; %h=0.01 M0=0.6; Pr=2/3; k1=1; k2=1.10; b1=0.375; b2=0.6; lambda=111.1532157006257798;
Integral_22= integral (@(x)((((1+(b1*(x.^2))).^((-k1)./(2*b1))).*((1+(b2*(x.^2))).^(k2./(2*b2)))).^lambda).*x,0,1);
for i=1:(n+1) x(i) = (i-0.5)*h ; end
for o=1:n
F1= @(x) ((((1+(b1*(x.^2))).^((-k1)./(2*b1))).*((1+(b2*(x.^2))).^(k2./(2*b2)))).^lambda).*x; Upper_Integral(o)= quadl(F1,0,x(o)); V(o)= Upper_Integral(o)./(x(o).*Integral_22); F2= @(x) ((-lambda).*(((k1*x)./(1+(b1*(x.^2))))-((k2*x)./(1+(b2*(x.^2)))))); U(o)=F2(x(o)); F3= @(x)((((1+(b1*(x.^2))).^((-k1)./(2*b1))).*((1+(b2*(x.^2))).^(k2./(2*b2)))).^lambda); F4= @(x) ((((1+(b1*(x.^2))).^((-k1)./(2*b1))).*((1+(b2*(x.^2))).^(k2./(2*b2)))).^lambda).*x; Upper_Integral2(o)= quadl(F4,0,x(o)); F5(o)= -((2./(x(o)).^2).*Upper_Integral2(o)); F6(o)=F3(x(o)); f(o)=((1./Integral_22).*(F5(o)+F6(o))).^2; w=@(x)(((((1+(b1*(x.^2))).^(((Pr)*k1)./(2*b1)))./((1+(b2*(x.^2))).^(((Pr)*k2)./(2*b2)))).^lambda).*((U(o).*(V(o).^2))+(x.*f(o)))); Integral(o)=quad(w,0,x(o)); d_Theta=@(x) (-(((((1+(b2*(x.^2))).^(((Pr)*k2)./(2*b2)))./((((1+(b1*(x.^2))).^(((Pr)*k1)./(2*b1)))))).^lambda).*(1/x).*Integral(o).*((M0.^2).*(Pr).*(gamma-1)))); F9(o)=d_Theta(x(o));
end
• Warning: Maximum function count exceeded; singularity likely. > In quad at 99 *
I think that the problem is at the line Integral(o)=quad(w,0,x(o));

Mike Hosea on 30 Sep 2014
Is there some important reason why you are using INTEGRAL, QUAD, and QUADL, all three? QUAD and QUADL are deprecated. Use INTEGRAL for every case. Literally just substitute "integral" for "quad" and "quadl". INTEGRAL can even handle mild endpoint singularities, which QUAD and QUADL cannot. I tried it on your problem and there were no problems.
FANI on 30 Sep 2014
You are right...Thank you Mike...