Why the if statement does not work when I am trying to avoid the singularity in my code ??

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Avan Al-Saffar 2014-11-17

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https://ww2.mathworks.cn/matlabcentral/answers/163046-why-the-if-statement-does-not-work-when-i-am-trying-to-avoid-the-singularity-in-my-code

编辑： Avan Al-Saffar 2014-12-3

function RunlogisticOscilnumericalfisherfixedn0omega
omega=1;
N0=1;
k = 10;
A = 1;
p0 = 0.1;
tspan=(0:0.1:4);
[t,p] = ode45(@logisticOscilnumerical,tspan,p0,[],omega,k,N0);
P = @(T) interp1(t,p,T);
f = @(t)  (  ( A.*( ( N0.* (sin(omega.*t)).^2 .*(1-(2.*P(t)./k))+(omega.*cos(omega.*t) ) ).^2 ) ./( (N0.^2).*((sin(omega.*t)).^4).*((P(t)-(P(t).^2./k)).^2 )) ) ) ;

v = ( (N0.^2).*((sin(omega.*t)).^4).*((P(t)-(P(t).^2./k)).^2 )); if v <= 1e-100

      f = 0
else
      f = I4
end
                                                                                I1 = integral( f, 0.01,1,'ArrayValued',true)./1
I2 = integral( f, 0.01,2,'ArrayValued',true)./2
I3 = integral( f, 0.01,3,'ArrayValued',true)./3
I4 = integral( f, 0.01,4,'ArrayValued',true)./4
I=[I1,I2,I3,I4] ;
T=[1,2,3,4] ;
figure(2)
plot(T,I)
g = @(t) (  ( A.*( ( N0.* (sin(omega.*t)).^2 .*(1-(2.*P(t)./k))+(omega.*cos(omega.*t) ) ).^2 ) ./( (N0.^2).*((sin(omega.*t)).^4).*((P(t)-(P(t).^2./k)).^2 )) ) ) ;
figure(3)
plot(tspan,g(tspan))
1;
% function dpdt = logisticOscilnumerical(t,p,omega,k,N0) 
% dpdt = N0*sin(omega*t)*p*(1-p/k);
% end

Could anyone help me to avoid singularity at x = 3.14159 using if statement please??

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Avan Al-Saffar 2014-11-28

Ok, I know that my problem is with the term(sin(omega*t) but what if I tried to use if statement to avoid integration at those specific values, What do you think? Or do you have another idea?

Regards

Avan

Torsten 2014-11-28

The values of a function at a finite number of points do not influence the integral.

Changing the function in a neighborhood of the singularities will give you a finite value for the integrals, but this finite value will depend on the size of the neighborhood you chose.

So I think it is better to reconsider how you came up with the function f and if this f is appropriate for your purpose.

Best wishes

Torsten.

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