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

 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));

Anyone can help please?

Answer 1

[Mike Hosea]

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]

You are right...Thank you Mike...