Tweeted twitter.com/#!/StackMma/status/258992968185311233 occurred Oct 18 '12 at 18:08 4 added 227 characters in body edited Oct 18 '12 at 13:28 fpghost 91511 gold badge1111 silver badges2121 bronze badges 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. 3 deleted 81 characters in body edited Oct 18 '12 at 12:28 Mr.Wizard♦ 235k3030 gold badges488488 silver badges10901090 bronze badges 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? 2 edited tags | link edited Oct 18 '12 at 12:23 J. M. will be back soon♦ 101k1010 gold badges317317 silver badges477477 bronze badges 1 asked Oct 18 '12 at 12:21 fpghost 91511 gold badge1111 silver badges2121 bronze badges