Is there anyway to remove the noise from the graph in Mathematica?

Question

I am trying to find the root of an equation in Mathematica. But am unable to find it. The Plot function gives a very noisy graph. Can anyone please provide me with a solution to this

    A10=

-0.24999999999999997` (2.611333478147288`*^17 \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
        7.658922220148525`*^-18 P)^0.5`)^1.` + 
   2.611333478147288`*^17 (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
        7.658922220148525`*^-18 P)^0.5`)^1.`) \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
     7.658922220148525`*^-18 P)^0.5`)^0.5` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
     7.658922220148525`*^-18 P)^0.5`)^0.5` (-5.3376918284751424`*^26 \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
        7.658922220148525`*^-18 P)^0.5`)^1.5` Cosh[
     204404.83274706744` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`] Sin[
     204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
          7.658922220148525`*^-18 P)^0.5`)^0.5`] Sinh[
     183964.3494723607` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`]^2 + 
   Sinh[204404.83274706744` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
          7.658922220148525`*^-18 P)^0.5`)^0.5`] \
(2.6688459142375712`*^26 (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^1.5` (Cos[
          163523.86619765396` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`] - 
         Cos[204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`]) + 
      5.222666956294576`*^17 (2.611333478147288`*^17 \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
              7.658922220148525`*^-18 P)^0.5`)^1.` + 
         2.611333478147288`*^17 (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
              7.658922220148525`*^-18 P)^0.5`)^1.`) (-0.000072` + 
         5.2226669562945766`*^13 (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
              7.658922220148525`*^-18 P)^0.5`)^1.` \
(9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 

              7.658922220148525`*^-18 P)^0.5`)^1.`) \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
           7.658922220148525`*^-18 P)^0.5`)^0.5` \
(9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
           7.658922220148525`*^-18 P)^0.5`)^0.5` Sin[
        204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`] + 
      2.6688459142375712`*^26 (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^1.5` Sin[
        204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
             7.658922220148525`*^-18 P)^0.5`)^0.5`] Sinh[
        367928.6989447214` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`]))

    Plot[A10, {P, 0, 10}]

Is there any way to improve the accuracy of the plot.

I couldnt get you...could you please be a bit more specific about Remove [A10,P] — Saquib Mohammed Haroon, Jul 07 '18 at 14:38
@Coolwater is saying: "Evaluate Remove[A10, P], then try to evaluate your code again" (Remove clears any definitions that might still float around from earlier) — Lukas Lang, Jul 07 '18 at 14:43
There is no other definition. I need to plot the equation A10 so as to find the smallest root arising from this equation. But with this present plot, it is impossible to detect the smallest root — Saquib Mohammed Haroon, Jul 07 '18 at 14:48
It works fine in Mathematica 10.4. Nice smooth plot with zeros at 0 and around 5.75. — JimB, Jul 07 '18 at 14:56
I have been using Mathematica 11.0. It gives a very noisy plot. Ill check out in 10.4 — Saquib Mohammed Haroon, Jul 07 '18 at 15:02
Ive edited the equation. The equation was rounded one when i copied but if the equation is not rounded off.. Then the equation gives the following noisy curve — Saquib Mohammed Haroon, Jul 07 '18 at 16:28
Possible duplicate: https://mathematica.stackexchange.com/questions/3152/funny-behaviour-when-plotting-a-polynomial-of-high-degree-and-large-coefficients — Michael E2, Jul 08 '18 at 01:04

score 3 · Accepted Answer · answered Jul 08 '18 at 00:12

$Version

(* "11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)" *)

A10 = -0.24999999999999997` (2.611333478147288`*^17 (-9.305307031664072`*^-8 \
+ (8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^1.` + 
     2.611333478147288`*^17 (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
            7.658922220148525`*^-18 P)^0.5`)^1.`) (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
         7.658922220148525`*^-18 P)^0.5`)^0.5` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
         7.658922220148525`*^-18 P)^0.5`)^0.5` (-5.3376918284751424`*^26 \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
            7.658922220148525`*^-18 P)^0.5`)^1.5` Cosh[
       204404.83274706744` (9.305307031664072`*^-8 + (8.658873895353684`*^-15 \
+ 7.658922220148525`*^-18 P)^0.5`)^0.5`] Sin[
       204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`] Sinh[
        183964.3494723607` (9.305307031664072`*^-8 + (8.658873895353684`*^-15 \
+ 7.658922220148525`*^-18 P)^0.5`)^0.5`]^2 + 
     Sinh[204404.83274706744` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
              7.658922220148525`*^-18 P)^0.5`)^0.5`] (2.6688459142375712`*^26 \
(9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
               7.658922220148525`*^-18 P)^0.5`)^1.5` (Cos[
            163523.86619765396` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`] - 
           Cos[204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`]) + 
        5.222666956294576`*^17 (2.611333478147288`*^17 \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
                  7.658922220148525`*^-18 P)^0.5`)^1.` + 
           2.611333478147288`*^17 (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
                  7.658922220148525`*^-18 P)^0.5`)^1.`) (-0.000072` + 
           5.2226669562945766`*^13 (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 
                  7.658922220148525`*^-18 P)^0.5`)^1.` \
(9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 

                  7.658922220148525`*^-18 P)^0.5`)^1.`) \
(-9.305307031664072`*^-8 + (8.658873895353684`*^-15 + 
               7.658922220148525`*^-18 P)^0.5`)^0.5` (9.305307031664072`*^-8 \
+ (8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5` Sin[
          204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`] + 
        2.6688459142375712`*^26 (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^1.5` Sin[
          204404.83274706744` (-9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`] Sinh[
          367928.6989447214` (9.305307031664072`*^-8 + \
(8.658873895353684`*^-15 + 7.658922220148525`*^-18 P)^0.5`)^0.5`]));

Rationalize and Simplify the expression

A10r = A10 // Rationalize[#, 0] & // Simplify;

Use high precision in the Plot

Plot[A10r, {P, 0, 10}, WorkingPrecision -> 70]

Use FindRoot with high precision; however, precision is reduced for display of results.

(FindRoot[A10r, {P, #}, WorkingPrecision -> 70] & /@ {10^-10, 58/10}) // N

(* {{P -> -8.4392*10^-14}, {P -> 5.78585}} *)

Is there anyway to remove the noise from the graph in Mathematica?

1 Answers1