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I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on here:

Given the definitions

v = 0.6;
g = 1/Sqrt[1 - v^2];

ig[tau1_?NumericQ, tau2_?NumericQ, ωω_?NumericQ, ll_?IntegerQ] :=
(((2 ll + 1) ωω)/(4 Pi^2)) *
 SphericalBesselJ[ll, ωω v g tau1] *
 SphericalBesselJ[ll, ωω v g tau2] *
 Exp[-I ωω g (tau1 - tau2)];

I would like to numerically integrate this:

f[ω_, l_, pg_, wp_] := 
 2 Re[NIntegrate[
    Exp[-I 1 s] ig[100, 100 - s, ω, l], {s, 0, 40}, 
    PrecisionGoal -> pg, WorkingPrecision -> wp, MaxRecursion -> 20]]

But for example f[2, 1, 15, 25] etc I get a host of errors like ::slwcon,::einc.

I was wondering if I could use "LevinRule" here and if so what would the options be?

I believe the problem gets worse at large $\omega$ maybe 100 or more. Where even putting the WorkingPrecision upto 40 and PrecisionGoal down to 10, things still scream, if I generate a table of these from 1 to 100 in omega.

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on here:

Given the definitions

v = 0.6;
g = 1/Sqrt[1 - v^2];

ig[tau1_?NumericQ, tau2_?NumericQ, ωω_?NumericQ, ll_?IntegerQ] :=
(((2 ll + 1) ωω)/(4 Pi^2)) *
 SphericalBesselJ[ll, ωω v g tau1] *
 SphericalBesselJ[ll, ωω v g tau2] *
 Exp[-I ωω g (tau1 - tau2)];

I would like to numerically integrate this:

f[ω_, l_, pg_, wp_] := 
 2 Re[NIntegrate[
    Exp[-I 1 s] ig[100, 100 - s, ω, l], {s, 0, 40}, 
    PrecisionGoal -> pg, WorkingPrecision -> wp, MaxRecursion -> 20]]

But for example f[2, 1, 15, 25] etc I get a host of errors like ::slwcon,::einc.

I was wondering if I could use "LevinRule" here and if so what would the options be?

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on here:

Given the definitions

v = 0.6;
g = 1/Sqrt[1 - v^2];

ig[tau1_?NumericQ, tau2_?NumericQ, ωω_?NumericQ, ll_?IntegerQ] :=
(((2 ll + 1) ωω)/(4 Pi^2)) *
 SphericalBesselJ[ll, ωω v g tau1] *
 SphericalBesselJ[ll, ωω v g tau2] *
 Exp[-I ωω g (tau1 - tau2)];

I would like to numerically integrate this:

f[ω_, l_, pg_, wp_] := 
 2 Re[NIntegrate[
    Exp[-I 1 s] ig[100, 100 - s, ω, l], {s, 0, 40}, 
    PrecisionGoal -> pg, WorkingPrecision -> wp, MaxRecursion -> 20]]

But for example f[2, 1, 15, 25] etc I get a host of errors like ::slwcon,::einc.

I was wondering if I could use "LevinRule" here and if so what would the options be?

I believe the problem gets worse at large $\omega$ maybe 100 or more. Where even putting the WorkingPrecision upto 40 and PrecisionGoal down to 10, things still scream, if I generate a table of these from 1 to 100 in omega.

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I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on here:

Given the definitions

v = 0.6;
g = 1/Sqrt[1 - v^2];

ig[tau1_?NumericQ, 
 tau2_?NumericQ, \[Omega]\[Omega]_ωω_?NumericQ, 
 ll_?IntegerQ] :=  
(((2 ll + 1) \[Omega]\[Omega]ωω)/(
 4 Pi^2)) SphericalBesselJ[*
ll SphericalBesselJ[ll, \[Omega]\[Omega]ωω v g tau1] SphericalBesselJ[*
ll SphericalBesselJ[ll, \[Omega]\[Omega]ωω v g tau2] *
 Exp[-I \[Omega]\[Omega]ωω g (tau1 - 
   tau2)];

I would like to numerically integrate this:

f[\[Omega]_f[ω_, l_, pg_, wp_] := 
 2 Re[NIntegrate[
    Exp[-I 1 s] ig[100, 100 - s, \[Omega]ω, l] , {s, 0, 40}, 
    PrecisionGoal -> pg, WorkingPrecision -> wp, MaxRecursion -> 20]]

But for example f[2, 1, 15, 25]f[2, 1, 15, 25] etc I get a host of errors like ::slwcon::slwcon,::einc::einc.

I was wondering if I could use "LevinRule" here and if so what would the options be?

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on here:

Given the definitions

v = 0.6;
g = 1/Sqrt[1 - v^2];

ig[tau1_?NumericQ, 
 tau2_?NumericQ, \[Omega]\[Omega]_?NumericQ, 
 ll_?IntegerQ] := (((2 ll + 1) \[Omega]\[Omega])/(
 4 Pi^2)) SphericalBesselJ[
ll, \[Omega]\[Omega] v g tau1] SphericalBesselJ[
ll, \[Omega]\[Omega] v g tau2]  Exp[-I \[Omega]\[Omega] g (tau1 - 
   tau2)];

I would like to numerically integrate this:

f[\[Omega]_, l_, pg_, wp_] := 
2 Re[NIntegrate[
Exp[-I 1 s] ig[100, 100 - s, \[Omega], l] , {s, 0, 40}, 
PrecisionGoal -> pg, WorkingPrecision -> wp, MaxRecursion -> 20]]

But for example f[2, 1, 15, 25] etc I get a host of errors like ::slwcon,::einc.

I was wondering if I could use "LevinRule" here and if so what would the options be?

I'm currently looking at a simplified problem that approximates another problem I'm looking into. In this simplified problem I at least have an analytic integrand and can easily provide all info on here:

Given the definitions

v = 0.6;
g = 1/Sqrt[1 - v^2];

ig[tau1_?NumericQ, tau2_?NumericQ, ωω_?NumericQ, ll_?IntegerQ] := 
(((2 ll + 1) ωω)/(4 Pi^2)) *
 SphericalBesselJ[ll, ωω v g tau1] *
 SphericalBesselJ[ll, ωω v g tau2] *
 Exp[-I ωω g (tau1 - tau2)];

I would like to numerically integrate this:

f[ω_, l_, pg_, wp_] := 
 2 Re[NIntegrate[
    Exp[-I 1 s] ig[100, 100 - s, ω, l], {s, 0, 40}, 
    PrecisionGoal -> pg, WorkingPrecision -> wp, MaxRecursion -> 20]]

But for example f[2, 1, 15, 25] etc I get a host of errors like ::slwcon,::einc.

I was wondering if I could use "LevinRule" here and if so what would the options be?

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