Items tagged with roots roots Tagged Items Feed

Hi, 

 

I wish to be able to calculate the roots of the function f(p) by using the roots of the function h(p) and applying the bisection method due to the fact that the roots of h(p) bracket the roots of f(p) as can be seen in the graph below. I have done this before for another example when h:=J0(p); and hence i could use The commands BesselJZeros(0,n)/BesselJZzeros(0,n+1) to find the roots. So my problem arises with the finding the roots of h(p) and how to insert them into my bisection loop(underlined below).

Any advice would amazing. Many thanks


restart;

Digits := 30:
with (plots):
with(RootFinding):

#Define given parameters

R:=1: #external radius of particles, cm

d:=10^(-3): #diffusivity cm^2 per second

alpha:= 1: #fractional void volume

c0:=10^(-6): #concentartion of soltion in void volume of solid initially, moles per liter

C0:=0: #concentration of main body of solution initially, moles per liter

k1:=0.5: #constant in adsorption isotherm (ka)

k2:=0.75: #constant in adsorption isotherm (kd)

k:=2.5: #equilbrium constant for adsorption kinetics

n0:=(k1/k2)*c0:#initial amount absrobed on solid, moles per liter

V:=0.1: #volume of external solution, liters

W:=0.1: #weight of absorbant, grams

rho:=2.0: #solid aparrant density, g/cc

delta:=(1/d)*((p+alpha*k2+k1)/(p+alpha*k2));

beta:=W*alpha*d/(rho*V);

   

1000*(p+1.25)/(p+.75)

 

0.500000000000000000000000000000e-3

 

 

 

 

 


f:=p->(BesselJ(0,R*sqrt(-delta*p))*k*p-(R*sqrt(-delta*p))*BesselJ(1,R*sqrt(-delta*p))*(d*p/R + 2*beta*k/(R^2)));

proc (p) options operator, arrow; BesselJ(0, R*sqrt(-delta*p))*k*p-R*sqrt(-delta*p)*BesselJ(1, R*sqrt(-delta*p))*(d*p/R+2*beta*k/R^2) end proc

(2)

h:=p->(BesselJ(0,R*sqrt(-delta*p)));
plot([f(p),h(p)],p=-0.3..0,axis=-5..5,legend=["f(p)","h(p)"]);


 




proc (p) options operator, arrow; BesselJ(0, R*sqrt(-delta*p)) end proc

 

 

 

(3)



points:=5:
rts:= Array(1..points):
for n from 1 by +1 to points do
pl:=evalf(#**first root of h**);
pu:=evalf(#**second root of h, i.e n+1 root**);
pe:= (pl+pu)/2;
while abs(f(pe))>10^(-6) do
pe:=(pu+pl)/2;
if f(pu)*f(pe) <0 then
pl:=pe;
elif f(pl)*f(pe)<0 then
pu:=pe;
end if;
od;
rts[n]:=pe;

od;
rts[n]:=p[n];

 

 

Download spherical_continue.mw


 

Download spherical_continue.mw

restart:

lambda1:=(1/(K+2))*(S+sqrt(2*alpha*(K+2)+S^2));

lambda2:=(1/(K+2))*(S-sqrt(2*alpha*(K+2)+S^2));

where K>=0, S (-15, 15) and alpha (-15, 15). While plotting for small values of S and alpha, I get complex roots.

  • How we can avoid the complex roots?
  • Is it possible to impose a condition in plotting? 

    solve(lambda1=lambda2,S);

    solve(lambda1=lambda2,alpha);

    solve(lambda1=lambda2,K);

  • How to single out the range of S and alpha for which we have complex roots?

Thanks

 

Hi there,
i am currently using maple5 as a new student in mathematics in the university. I am trying to know how to use maple5 to programme finding roots of quadratic equation. can anyone point me in the right direction?? Perhaps a book or a website on maple5. I know its old version but that's what we are allowed to use in my university and i'm new to this. Thanks

Real roots only...

January 17 2014 Syeda 25

I want to find real roots only.  Cannot we find a simplified formula for x in this case which gives only real roots? 

 

 

``

eq1 := a^2*x^3+Typesetting:-delayDotProduct(2*a*b-Typesetting:-delayDotProduct(a^2, e), x^2)+(-2*a*b*c^2-a*c+b^2)*x-c*b-d-b^2*e = 0:

``

# Formula

eq2 := A*x^3+B*x^2+C*x+E = 0:

``

NULL

a := .7438:

b := 15.12*z[1]+10.85*z[1]^2:

c := 18.92-17.76*z[2]:

d := -.9224:

e := 2.106-5.317*z[2]+2.87*z[2]^2:NULL

NULL

A := a^2:

B := -a^2*e+2*a*b:

C := -2*a*b*e^2-a*c+b^2:

E := -b^2*e-b*c-d:

``

eq2

.55323844*x^3+(-1.165120155+2.941568785*z[2]-1.587794323*z[2]^2+22.492512*z[1]+16.140460*z[1]^2)*x^2+(-1.4876*(15.12*z[1]+10.85*z[1]^2)*(2.106-5.317*z[2]+2.87*z[2]^2)^2-14.072696+13.209888*z[2]+(15.12*z[1]+10.85*z[1]^2)^2)*x-(15.12*z[1]+10.85*z[1]^2)^2*(2.106-5.317*z[2]+2.87*z[2]^2)-(15.12*z[1]+10.85*z[1]^2)*(18.92-17.76*z[2])+.9224 = 0

(1)

``

``# Putting z1 and z2 value

"(->)"

.55323844*x^3+14.11629660*x^2+83.26002702*x-3.52866181 = 0

(2)

 

"(->)"

[[x = 0.4208050385e-1], [x = -9.354079555], [x = -16.20375615]]

(3)

``

``

 

Download cubic.mw

I am trying to use Maple17 to create practice integration problems in which the integrands contain square roots.  I want the students to practice converting square roots, perhaps with fractions, to fractional and/or negative powers.  Hopefully Maple can typeset the integrals if I use the inert form "Int", and also do the integrals for me so I can find the answers quicker than doing it by hand, and not have to worry about making a careless mistake.  The trouble is, Maple is converting the square roots to fractional exponents:

Download DisplaySquareRoot.

Download DisplaySquareRoot.mw

I hope at least one of these works.  To make a long story short, when I display an integral using "Int", how do I prevent Maple from converting square roots to fractional exponents?

 

GS

 

 

I have a matrix A4  

I have reason to believe that the expression below is a real number: 

(1/6)*(-108+(12*I)*sqrt(1419))^(1/3)+10/(-108+(12*I)*sqrt(1419))^(1/3)+1;

A numerical approximation supports that. How can Maple help here to get a simplified expression?

t0 := arccosh(lambda/(s*(1-lambda)))

f := int(sqrt(lambda-s*cosh(t)/(1+s*cosh(t))), t = -t0 .. t0)

s := 1/10

with(Student[Calculus1])

g := f-Pi*(0+1/2)

Roots(g, lambda = 0 .. 1, numeric)

Why does maple say:

Error, (in mod/Expand) too many levels of recursion?

Dear All,

evalf(RoofOf(Z^6-3*Z^4+3*Z^2+Z-1,index=real[2]) fails to deliver a numerical value.

  1. I can use fsolve to compute the real roots but I need to replace all the occurences of RootOf by its numerical value in lengthy expressions.
  2. Also simplify(RoofOf(Z^6-3*Z^4+3*Z^2+Z-1,index=real[2],RootOf) does not work.
  3. I read the other posts related but could not find any answer.

Thanks for any help,

S.

 

 I want to calculate successive roots of the following complex eq.

how can I set interval (?) for fsolve in the following code:

I'm solving a system of ordinary differential equations numerically, I used the dsolve(system,numeric) to do it. I have also plotted the solutions. Now I want to know where does this solution cross zero and use this value for later computations, is there a way to do it? 

This question is, as I think, equivalent to how to find the roots for a curve expressed in numerical arrays.

Thank you!

I have a solution with RootOF(_Z^6+....). I do not need to find the roots explicitly(I know that I should use 'allvalues' to find the roots). My question is "Is it okay if I use RootOF(...) expression in another equation without finding the roots explicitly? I mean does RootOF(_Z^6+...) stand for all its roots and can it be used for each roots?"

Thank you in advance.

Good day, dear Friends!

I'm trying to find real positive roots  of equation 

sqrt(x+3-4*sqrt(x-1))+sqrt(x+8-6*sqrt(x-1)) = 1 with Maple 16.01.

One can easly verifies that this euqation has at least two positive  real (integer) solutions: at x=5 and x=10,

but Maple function 

I am using the function solve() to find roots of a trig. equation. Such as for sin(k*x) = 0, Maple retuns x = 0, whereas I expecting to get  x = n ∏/k, for n = 0,1,2,.... I am sorry I am new to Maple, can anyone help me get what I am looking for?

Thank you

I want to solve two equations with all roots.

eq1:=-7.506556000*10^(-23)*omega^12+2.243366854*10^(-78)*omega^34+3.651941282*10^(-50)*omega^25+1.145341958*10^(-105)*omega^41-3.837716260*10^(-102)*omega^40+9.952750000*10^(-10)*omega^5+2.520327960*10^(-113)*omega^43-5.961864252*10^(-98)*omega^39+2.934254874*10^(-60)*omega^29+3.877088344*10^(-109)*omega^42-3.482296310*10^(-82)*omega^35+2.846747460*10^(-123)*omega^45-1.089582984*10^(-70)*omega^32-5.927854900*10^(-48...

1 2 Page 1 of 2