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I am trying to plot this function numerically. R2T = (0.0634921 (25. -10. R+1. R^2) (-125.-75. R+153.75 R^2+79. R^3-30.75 R^4-3. R^5+1. R^6) (625. +812.5 R-631.25 R^2-1008.12 R^3+31. R^4+201.625 R^5-25.25 R^6-6.5 R^7+1. R^8) (-4.88281*10^6-732422. R+1.95312*10^7 R^2+1.49902*10^6 R^3-3.08374*10^7 R^4+591528. R^5+2.40886*10^7 R^6-3.43795*10^6 R^7-9.34819*10^6 R^8+2.80522*10^6 R^9+1.41155*10^6 R^10-761365. R^11+44421.9 R^12+35889.5 R^13-7601.87 R^14+108.687 R^15+139.25 R^16-19.875 R^17+1. R^18+R (-976562.-585937. R+3.30078*10^6 R^2+1.98437*10^6 R^3-4.15088*10^6 R^4-2.42229*10^6 R^5+2.38528*10^6 R^6+1.25652*10^6 R^7-647720. R^8-251304. R^9+95411.2 R^10+19378.3 R^11-6641.41 R^12-635. R^13+211.25 R^14+7.5 R^15-2.5 R^16) Cos[0.666667 \[Phi]]) (25. +1. R^2-10. R Cos[(2 \[Phi])/3]))/(2.27065*10^13+2.42203*10^12 R-1.88192*10^14 R^2-1.38661*10^13 R^3+6.94889*10^14 R^4+2.07061*10^13 R^5-1.50448*10^15 R^6+4.04723*10^13 R^7+2.11309*10^15 R^8-2.08736*10^14 R^9-2.00744*10^15 R^10+3.79735*10^14 R^11+1.2985*10^15 R^12-3.95153*10^14 R^13-5.5431*10^14 R^14+2.56059*10^14 R^15+1.39409*10^14 R^16-1.03105*10^14 R^17-1.14135*10^13 R^18+2.4023*10^13 R^19-3.75763*10^12 R^20-2.55967*10^12 R^21+1.07157*10^12 R^22-1.29768*10^10 R^23-7.72733*10^10 R^24+1.64917*10^10 R^25+7.25455*10^8 R^26-8.12296*10^8 R^27+1.12858*10^8 R^28+5.14506*10^6 R^29-3.50294*10^6 R^30+411464. R^31-56.7361 R^32-5429.44 R^33+684.762 R^34-40.127 R^35+1. R^36+R (5.44957*10^12+5.57067*10^12 R-3.73477*10^13 R^2-3.75172*10^13 R^3+1.12919*10^14 R^4+1.09276*10^14 R^5-1.99683*10^14 R^6-1.79842*10^14 R^7+2.31945*10^14 R^8+1.83225*10^14 R^9-1.89256*10^14 R^10-1.18794*10^14 R^11+1.13093*10^14 R^12+4.80866*10^13 R^13-5.00486*10^13 R^14-1.08935*10^13 R^15+1.58927*10^13 R^16+6.24809*10^11 R^17-3.36476*10^12 R^18+3.5343*10^11 R^19+4.27401*10^11 R^20-9.9325*10^10 R^21-2.68297*10^10 R^22+1.08649*10^10 R^23+3.78632*10^8 R^24-5.87792*10^8 R^25+4.62274*10^7 R^26+1.50145*10^7 R^27-2.70882*10^6 R^28-78427.4 R^29+55541.2 R^30-3789.68 R^31-300. R^32+55.5556 R^33-2.38095 R^34) Cos[(2 \[Phi])/3]+R Cos[0.666667 \[Phi]] (5.44957*10^12+5.57067*10^12 R-3.73477*10^13 R^2-3.75172*10^13 R^3+1.12919*10^14 R^4+1.09276*10^14 R^5-1.99683*10^14 R^6-1.79842*10^14 R^7+2.31945*10^14 R^8+1.83225*10^14 R^9-1.89256*10^14 R^10-1.18794*10^14 R^11+1.13093*10^14 R^12+4.80866*10^13 R^13-5.00486*10^13 R^14-1.08935*10^13 R^15+1.58927*10^13 R^16+6.24809*10^11 R^17-3.36476*10^12 R^18+3.5343*10^11 R^19+4.27401*10^11 R^20-9.9325*10^10 R^21-2.68297*10^10 R^22+1.08649*10^10 R^23+3.78632*10^8 R^24-5.87792*10^8 R^25+4.62274*10^7 R^26+1.50145*10^7 R^27-2.70882*10^6 R^28-78427.4 R^29+55541.2 R^30-3789.68 R^31-300. R^32+55.5556 R^33-2.38095 R^34+R (7.26609*10^11+3.87525*10^11 R-5.37691*10^12 R^2-2.99363*10^12 R^3+1.74631*10^13 R^4+1.0059*10^13 R^5-3.26414*10^13 R^6-1.92555*10^13 R^7+3.87181*10^13 R^8+2.30868*10^13 R^9-3.03595*10^13 R^10-1.79494*10^13 R^11+1.59681*10^13 R^12+9.06985*10^12 R^13-5.65667*10^12 R^14-2.92194*10^12 R^15+1.36118*10^12 R^16+5.84388*10^11 R^17-2.26267*10^11 R^18-7.25588*10^10 R^19+2.55489*10^10 R^20+5.74381*10^9 R^21-1.94301*10^9 R^22-2.95511*10^8 R^23+9.91184*10^7 R^24+9.85882*10^6 R^25-3.34248*10^6 R^26-206008. R^27+71528.8 R^28+2452.38 R^29-880.952 R^30-12.6984 R^31+4.7619 R^32) Cos[(2 \[Phi])/3]))

First, I have to do the integration from Phi = 0 to 2 pi by numerical integration. Then, plot the answer after integration concerning R from 0 to 1. My code is as follows

R2T0[R_?NumericQ] := 1/(2 \[Pi]) NIntegrate[Evaluate[R2T], {\[Phi], 0, 2 \[Pi]}] Plot[R2T0[R], {R, 0, 1}]. I am getting the following plot. As you can see, up to R = 0.6, the plot is smooth, after that, it is oscillating, which is not expected

As you can see, up to R = 0.6, the plot is smooth, after that, it is oscillating, which is not expected. The plot should be continous after R=0.6, so what is the problem. Please, someone, look into this.

J. M.'s missing motivation
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sachiraj mishra
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  • At first glance, it looks like this: https://mathematica.stackexchange.com/questions/3152/funny-behaviour-when-plotting-a-polynomial-of-high-degree-and-large-coefficients – Michael E2 May 21 '22 at 15:30
  • Plot Plot3D[R2T, {R, 0, 1}, {\[Phi], 0, 2 Pi}, PlotRange -> 2000, PlotPoints -> 100] and Plot[R2T /. R -> .7, {\[Phi], 0, 2 Pi}, PlotRange -> 100, PlotPoints -> 100] to see, Integration over phi runs into singularities, in some cases even two. You have to use , Method -> "PrincipalValue", Exclusions -> ... where the difficulty is to calculate exclusions, where Denominator[Together@R2T] ==0. – Akku14 May 21 '22 at 18:59
  • Akku14 can you please clarify a bit?? – sachiraj mishra May 22 '22 at 17:01
  • According to the suggestion given by Akku14, i tried to plot the function and saw the singularity at R=0.7. But i am not able to see where the singularity arises, is there any method to check where singularity is arising. – sachiraj mishra May 23 '22 at 07:54
  • One difficulty with the posted problem is that the coefficients have been rounded to six digits of precision. Given the size and signs of the coefficients, this could pose an obstruction to solving the problem. – Michael E2 May 23 '22 at 18:09

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