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I have a problem with numerical integration of this function. Integral value is zero, but NIntegrateNIntegrate[] needs a lot of time to calculate this. Is there any way to speed up this calculation?

Input:

Output:

During evaluation of In[4]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>

During evaluation of In[4]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained -1.49243*10^-14 and 1.0093478121591215*^-12 for the integral and error estimates. >>

Out[5]= {43.421484, -1.49243*10^-14}

Out[6]= {3.963227, 0}


All the best, Aleksandar

During evaluation of In[4]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>

During evaluation of In[4]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained -1.49243*10^-14 and 1.0093478121591215*^-12 for the integral and error estimates. >>

Out[5]= {43.421484, -1.49243*10^-14}

Out[6]= {3.963227, 0}


I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate needs a lot of time to calculate this. Is there any way to speed up this calculation?

Input

Output

During evaluation of In[4]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>

During evaluation of In[4]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained -1.49243*10^-14 and 1.0093478121591215*^-12 for the integral and error estimates. >>

Out[5]= {43.421484, -1.49243*10^-14}

Out[6]= {3.963227, 0}


All the best, Aleksandar

I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate[] needs a lot of time to calculate this. Is there any way to speed up this calculation?

Input:

Output:

During evaluation of In[4]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>

During evaluation of In[4]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained -1.49243*10^-14 and 1.0093478121591215*^-12 for the integral and error estimates. >>

Out[5]= {43.421484, -1.49243*10^-14}

Out[6]= {3.963227, 0}

1

# NIntegrate::slwcon Problem

I have a problem with numerical integration of this function. Integral value is zero, but NIntegrate needs a lot of time to calculate this. Is there any way to speed up this calculation?

Input

function[s_, t_] :=100 (-2160 (1 - 2 s)^4 t^3 (-2 + 5 t) +
96 (1 - 2 s) t^3 (25 (-1 + 2 s) t^2 (-3 + 5 t) +
5/4 (-1 + 2 s)^3 (-1 + 5 t)) -
24 (-1 + 2 s)^3 t (5 (-1 + 2 s) t^2 (-3 + 5 t) +
25/4 (-1 + 2 s)^3 (-1 + 5 t)));

AbsoluteTiming[NIntegrate[function[s, t], {t, 0, 1/2}, {s, 0, 1/2}]]
AbsoluteTiming[Integrate[function[s, t], {t, 0, 1/2}, {s, 0, 1/2}]]


Output

During evaluation of In[4]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>

During evaluation of In[4]:= NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained -1.49243*10^-14 and 1.0093478121591215*^-12 for the integral and error estimates. >>

Out[5]= {43.421484, -1.49243*10^-14}

Out[6]= {3.963227, 0}
`

All the best, Aleksandar