Axel Vogt

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17 years, 271 days
Munich, Germany

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These are replies submitted by Axel Vogt

@acer

Yes, I am using Windows. I "played" with it using some other solver and it works. Thus it may be a problem with fsolve for this task. And for example plotting is ok.

@fkohlhepp ok, now one should proceed with acer's approach, "alternative", https://www.mapleprimes.com/questions/234625-How-Do-You-Implement-Recursion#comment288258

which is based on Rouben's translation to Maple https://www.mapleprimes.com/questions/234625-How-Do-You-Implement-Recursion#answer288250

@acer 

Neat :-) However fsolve(IIf, 7..8) and U(6) unfortunately does not work for me using Maple 2021.2, the calls return unevaluated.

U(8.3) works

@Rouben Rostamian  

f:= r -> eqn2(6*Unit('degree'), r*Unit('m'/'sec'))/Unit(N);

# plot(f, 5 .. 10, numpoints=3); # ok

fsolve(f, 7 .. 8);
                        7.74974018709663

@fkohlhepp I do not know Maple Flow - but you may try to print / export as pdf

For that you may also try to replace lower case int(...) by Upper Case Int(...)

Edit: try to write
Thust := (theta, u) -> N__bld*Int(th__s(r, theta, u), r = R__hng .. R__tip);

Edit 2: moreover you may feed (your original) Thust with some test values to check whether you will get numerical values (otherwise fsolve can not work).

Yes, just eqn2(theta) should be enough (and we do not have or need your csv data).

Or complete the attached Maple sheet, MP_234625_1.mw

And it is likely the problem adressed by acer

@fkohlhepp 

You could print your final eqn(2) or your function (I mean print = ready for copy paste, not just a picture) and post it, no?

Well, it is on you

Why do you not upload a Maple Worksheet, just containing the mathematical equation and constants (without unit)?

Vbar(s) =

9/3200*(2^(4/5)*exp(4*s)+(-4/3*s-1)*2^(4/5))*exp(-4*s)*(exp(2)*2^(1/10)-1/10*(-\
1)^(9/10)*GAMMA(1/10,-2)+1/10/sin(1/10*Pi)*(-1)^(9/10)/GAMMA(9/10)*Pi)+9/3200*(
100/33*GAMMA(9/10)*2^(9/10)*WhittakerM(-1/20,11/20,4*s)*s^(1/20)*exp(2*s)*sin(1
/10*Pi)-800/11*GAMMA(9/10)*s^(11/10)*exp(4*s)*sin(1/10*Pi)+(320/3*exp(4*s)-320/
9)*Pi)*exp(-4*s)/Pi

Find the sheet attached, including some numerical cross check by plotting

MP_234576.mw

For Example 5 there is an easy but ugly workaround: decompose it


 

#

restart; interface(version);

Example 5 . Regular singular point. Complex roots

 

Order:=6;  
ode:=x^3*diff(y(x),x$2)+sin(x^3)*diff(y(x),x)+x*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0): # simplify(%);
sol1:=eval(%, _C2=0):
sol2:=eval(%%, _C1=0):

6

 

x^3*(diff(diff(y(x), x), x))+sin(x^3)*(diff(y(x), x))+x*y(x) = 0

(1.1)

'rhs(sol1)+rhs(sol2)= rhs(sol)';
is(%);

rhs(sol1)+rhs(sol2) = rhs(sol)

 

true

(1.2)

rhs(sol1):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

(1)

rhs(sol2):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

(2)

 


 

Download MP_234443_odetest_series_Example5.mw

@ecterrab Thank you, it is just that the FunctionAdvisor is a bit short (for me) in its condition for the definition, but reading again it becomes clear what is meant by e1,e2,e3

Done more carefully it is 3.60773264994268*10^29

Edit: uploaded according file
MP_234318_(2).mw

Have you estimated how many terms are involved?

 

Edit: moreover in one case you use LegendreP as summation index - that will not work. Try starting with "1" oder "2" instead of "9"

Here is a short way to get it in trigonometrics, like dharr, but using the parameters

# https://www.mapleprimes.com/questions/234277-How-To-Solve-A-Cubic-Assuming-Discriminant

restart;

f := 2*y^3*z - y^2 -2*m;
assume(m<0, 0<z); additionally(0 < discrim(f,y));

2*y^3*z-y^2-2*m

(1)

S:=[solve(f,y)]:

map(evalc@Im, S); # to show that all solutions are real

[0, 0, 0]

(2)

map(evalc@Re, S):
simplify(%, {discrim(f,y)=discr}): # more easy to read
Z:=simplify(%), discr = 'discrim(f,y)'; #%;

[(1/6)*(1+2*cos((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1)))/z, (1/6)*(-3^(1/2)*sin((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))-cos((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))+1)/z, (1/6)*(3^(1/2)*sin((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))-cos((1/3)*arctan(3*3^(1/2)*discr^(1/2)*z, 108*m*z^2+1))+1)/z], discr = discrim(f, y)

(3)

 

Download MP_234277_CubicSolve_(2).mw

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