tomleslie

Interesting...

Answered: tomleslie 13876

November 11 2021

0 0

ebcause I cannot reproduce the problem

I am (still) running Win7 - which might(?) explain the issue.

Ouside chance that the Physics Updates version may be having an impact: I don't keep this completely up-to-date

see the attached

>	interface(version); Physics:-Version();

$`The "Physics Updates" version in the MapleCloud is 1112. The version installed in this computer is 1069 created 2021, September 26, 10:58 hours Pacific Time, found in the directory C:\Users\TomLeslie\maple\toolbox\2021\Physics Updates\lib\`$

(1)

>

restart;

>

integrand:=(((-3*x^2-18*x-27)*exp(2)^2+(30*x^3+330*x^2+1170*x+1350)*exp(2)-75*x^4-1200*x^3-7050*x^2-18000*x-16875)*ln(x)+(12*x^2+54*x+81)*exp(2)^2+(-120*x^3-1106*x^2-3510*x-4050)*exp(2)+225*x^4+3560*x^3+20990*x^2+54000*x+50625)/((3*x^4+18*x^3+27*x^2)*exp(2)^2+(-30*x^5-330*x^4-1170*x^3-1350*x^2)*exp(2)+75*x^6+1200*x^5+7050*x^4+18000*x^3+16875*x^2);

print("First time");
int(integrand,x);

print("second time");
int(integrand,x);

(((-3*x^2-18*x-27)*(exp(2))^2+(30*x^3+330*x^2+1170*x+1350)*exp(2)-75*x^4-1200*x^3-7050*x^2-18000*x-16875)*ln(x)+(12*x^2+54*x+81)*(exp(2))^2+(-120*x^3-1106*x^2-3510*x-4050)*exp(2)+225*x^4+3560*x^3+20990*x^2+54000*x+50625)/((3*x^4+18*x^3+27*x^2)*(exp(2))^2+(-30*x^5-330*x^4-1170*x^3-1350*x^2)*exp(2)+75*x^6+1200*x^5+7050*x^4+18000*x^3+16875*x^2)

ln(x)/x+1/x+(15*x^2+(-4*exp(2)+356/3)*x-9*exp(2)+225)/(x*(x+3)*(exp(2)-5*x-25))

(2)

>

Download intProb.mw

Errr yes...

Answered: tomleslie 13876

November 10 2021

0 0

@vv

and I can think of (at least) three possibilities

Maple produces crap EPS (as well as crap pdf)
GIMP cannot import "good" EPS (assuming Maple can produce it)
GIMP cannot transform EPS to pdf

So where do you think the problem is?

I don't think so...

Answered: tomleslie 13876

November 10 2021

0 0

@vv

As I clearly stated I exported from Maple in Encapsulated Postscript and converted to PDF using GIMP.

Since this site will not display PDF content inline, I uploaded the pdf file as a link only.

I also converted this PDF to PNG, just for display on this site

No...

Answered: tomleslie 13876

November 08 2021

0 0

@The function

and I have to write some random crap here before this site will accept the answer

Don't understand...

Answered: tomleslie 13876

November 01 2021

0 0

@Alex0099

I have no idea what you mean by

It's clear, but I'm interested what how to analyze this psi(x) without maple, maybe you know some works of literature, references, i.e., you yourself should know how to get these coeffs?

I'm also not sure what you mean by

Do I understand correctly that this 4*l^2*sin(n*Pi/2) and l^2((-1^n)-1) the same thing?

One can easily examine the first few terms in both of these summations - see the attached

>

  restart:
  assume( l>0 ):
  interface(showassumed=0):
# set the PDE, ic(initial conds) and bc (boundary conds)

  pde := diff(u(x, t), t, t) = a^2*diff(u(x, t), x, x):
  ic := u(x, 0) = 0, D[2](u)(x, 0) = psi:
  bc := u(0, t) = 0, u(l, t) = 0:
#
# OP's original definition of psi had a typo
#
  psi := piecewise( 0 <= x and x <= l/2, x,
                    l/2 < x and x <= l, l - x
                  ):

  res := pdsolve([pde,ic,bc], HINT = TWS):
  seq( op([2,1], res), n=1..8);

4*l^2*sin(Pi*x/l)*sin(a*Pi*t/l)/(Pi^3*a), 0, -(4/27)*l^2*sin(3*Pi*x/l)*sin(3*a*Pi*t/l)/(Pi^3*a), 0, (4/125)*l^2*sin(5*Pi*x/l)*sin(5*a*Pi*t/l)/(Pi^3*a), 0, -(4/343)*l^2*sin(7*Pi*x/l)*sin(7*a*Pi*t/l)/(Pi^3*a), 0

(1)

>

  restart:
  assume( l>0 ):
  interface(showassumed=0):
# set the PDE, ic(initial conds) and bc (boundary conds)

  pde := diff(u(x, t), t, t) = a^2*diff(u(x, t), x, x):
  ic := u(x, 0) = 0, D[2](u)(x, 0) = psi:
  bc := u(-l/2, t) = 0, u(l/2, t) = 0: # change bcs to -l/2, l/2
#
# OP's original definition of psi had a typo
#
  psi := piecewise( -l/2 <= x and x <= 0, x,
                    0 < x and x <= l/2, l - x
                  ): # change piecewise fumction to -l/2, l/2

  res := pdsolve([pde,ic,bc], HINT = TWS):
  seq( op([2,1], res), n=1..8);

l^2*sin(2*Pi*x/l)*sin(2*a*Pi*t/l)/(Pi^2*a), 0, (1/9)*l^2*sin(6*Pi*x/l)*sin(6*a*Pi*t/l)/(Pi^2*a), 0, (1/25)*l^2*sin(10*Pi*x/l)*sin(10*a*Pi*t/l)/(Pi^2*a), 0, (1/49)*l^2*sin(14*Pi*x/l)*sin(14*a*Pi*t/l)/(Pi^2*a), 0

(2)

>

Download waveEq4.mw

The easy way...

Answered: tomleslie 13876

November 01 2021

0 0

@Alex0099

in my original worksheet - you just have to specify the boundary conditions at -l/2, l/2 as well as adjyst the piecewise definition, as shown in the attached

>

  restart;
  assume( l>0 ):
  interface(showassumed=0):
# set the PDE, ic(initial conds) and bc (boundary conds)

  pde := diff(u(x, t), t, t) = a^2*diff(u(x, t), x, x);
  ic := u(x, 0) = 0, D[2](u)(x, 0) = psi;
  bc := u(-l/2, t) = 0, u(l/2, t) = 0; # change bcs to -l/2, l/2
#
# OP's original definition of psi had a typo
#
  psi := piecewise( -l/2 <= x and x <= 0, x,
                    0 < x and x <= l/2, l - x
                  ); # change piecewise fumction to -l/2, l/2

  res := pdsolve([pde,ic,bc], HINT = TWS);

piecewise(-(1/2)*l <= x and x <= 0, x, 0 < x and x <= (1/2)*l, l-x)

u(x, t) = Sum(-(1/2)*l^2*((-1)^n-1)*sin(2*n*Pi*x/l)*sin(2*a*n*Pi*t/l)/(Pi^2*n^2*a), n = 1 .. infinity)

(1)

>

Download waveEq3.mw

Don't understand...

Answered: tomleslie 13876

November 01 2021

0 0

@Alex0099

why you want to do it the hard way - but since you do, maybe the attached will help

>

restart:
with(PDETools):

# set the PDE, ic(initial conds) and bc (boundary conds)
pde := diff(u(x, t), t, t) = a^2*diff(u(x, t), x, x):
ic := u(x, 0) = 0, D[2](u)(x, 0) = psi:
bc := u(0, t) = 0, u(l, t) = 0:
psi := piecewise(0 <= x and x <= l/2, x, l/2 < x and x <= l, l - x):

# using Fourier method for solving (I require use this methods)
res := pdsolve(pde, HINT = T(t)*X(x)):

ode1 := op(1, op(1, op(2, res))):

ode2 := op(2, op(1, op(2, res))):

ode2 := subs(_c[1] = -lambda, ode2):

# solve 2 ODE
# equation rely X(x)
dsolve({ode2, X(0) = 0}, X(x)):

sin(sqrt(lambda)*l) = 0:

solve(%, lambda, allsolutions):

lambda := (Pi*n/l)^2:

X := (x, n) -> sin(Pi*n*x/l):

# equation rely T(t)
ode1 := subs(_c[1] = -lambda, ode1):

dsolve({%, T(0) = 0}, T(t)):

T := (t, n) -> C1[n]*sin(Pi*n*a*t/l):

# write the general solutions

Un := (x, t, n) -> T(t, n)*X(x, n):

# Derivative of Un w.r.t t
DtUn := eval(diff(Un(x, t, n), t), t=0):

# Compute the Fourier coefficients

int(DtUn*sin(Pi*n*x/l), x=0..l) assuming l>0:
int(psi*sin(Pi*n*x/l), x=0..l) assuming l>0:
coeffVal:=simplify(isolate(%%=%, C1[n])) assuming n::nonnegint:
gensol:= sum( eval( T(t,n)*X(x,n),coeffVal), n=0..infinity);

sum(4*l^2*sin((1/2)*n*Pi)*sin(Pi*n*a*t/l)*sin(Pi*n*x/l)/(Pi^3*a*n^3), n = 0 .. infinity)

(1)

>

Download waveEq2.mw

It seems to give the same answer as the "simple2 version I posted earlier

Modification...

Answered: tomleslie 13876

October 30 2021

0 0

to my original worksheet which seems to handle your issues

Automatically loading the Units[Simple] subpackage

Variables

Physical parameters

(1.1.1)

(1.1.2)

(1.1.3)

(1.1.4)

(1.1.5)

(1.1.6)

Variables

(1.2.1)

(1.2.2)

(1.2.3)

(1.2.4)

(1.2.5)

(1.2.6)

(1.2.7)

Calculate water vapor

The formula used below comes from Huang 2018 "A Simple Accurate Formula for Calculating Saturation Vapor Pressure of Water and Ice"

(2.1)

"`P__s`(T):=(exp(34.494-4924.99/((T+237.1))))/((T+105)^(1.57))"

(2.2)

(2.3)

(2.4)

Temperature conversion PO2

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

(3.8)

"S(PO2,P50):=(((PO2/(P50))^(n))/(1+(PO2/(P50))^(n)))"

(3.9)

(3.10)

(3.11)

(3.12)

(3.13)

"`PO2__c`(S,P50):=(exp((ln((-S)/((S-1))))/(n))*P50)"

(3.14)

(3.15)

(3.16)

Calculation Mass Transfer

Solubility

k__c := 4.658*10^(-5)*1.01^(37-T__b)*Unit('mL'/'mmHg'*(1/'mL'))

(4.1.1)

k__p := 2.855*10^(-5)*1.01^(37-T__b)*Unit('mL'/'mmHg'*(1/'mL'))

(4.1.2)

(4.1.3)

"lambda(`PvO2__c`):=(1.34/(convert(k,unit_free))*convert(Hgb,unit_free) *(n/(convert(`P50__c`,unit_free)))*((convert(`PvO2__c`,unit_free))/(convert(`P50__c`,unit_free)))^((n-1))*(1/((1+((convert(`PvO2__c`, unit_free))/(convert(`P50__c`,unit_free)))^(n))^(2))))/(1000)"

(4.1.4)

(4.1.5)

Diffusivity

(4.2.1)

(4.2.2)

N := k__c/k__p

(4.2.3)

beta := (1/3)*(2/(1+(N*D__c/D__p-1)*(.283*(1/2)))+1/(1+(N*D__c/D__p-1)*(1-.283)))*(N*D__c/D__p-1)

(4.2.4)

`ϰ` := -(N*D__c/D__p-1-N*D__c*beta/D__p)/(N*D__c/D__p-1-beta)

(4.2.5)

R := Hct*(N*D__c/D__p-1)/(N*D__c/D__p+`ϰ`)

(4.2.6)

(4.2.7)

Deff := D__m/(1+lambda(PvO2__c))

(4.2.8)

Density

(4.3.1)

(4.3.2)

(4.3.3)

Viscosity

(4.4.1)

(4.4.2)

(4.4.3)

(4.4.4)

Dimensionless Numbers

N__re := Q__blood*d/((1-Void__f)*A__f*nu)

(4.5.1)

(4.5.2)

Differential Equation

Convert flow from mL/min to mL/s

(4.6.1)

Convert η from mPa*s to g/cm*s

(4.6.2)

a := 4*((1-Void__f)/convert(d, unit_free))^(1+`ϕ`)*(convert(A__f, unit_free)*convert(`η__c`, unit_free)/(convert(Q__bc, unit_free)*convert(rho, unit_free)))^`ϕ`*phi/(Void__f*(nu/D__m)^(2/3))

(4.6.3)

ODE := diff(P(x), x) = a*(P__b-P(x))/(1+lambda(P(x))^(2/3))

diff(P(x), x) = .1081111001*(P__b-P(x))/(1+1.846187058*(P(x)^1.7/(1+0.2439243816e-3*P(x)^2.7)^2)^(2/3))

(4.6.4)

(4.6.5)

$sol := dsolve(eval({IC, ODE}, P__b = 1.0), numeric); sol(convert(Bloodpath, unit_free)); eval(P(x), sol(convert(Bloodpath, unit_free))); plots:-odeplot(sol, [x, P(x)], x = 0 .. convert(Bloodpath, unit_free))$

Download odeProb2.mw

No you didn't...

Answered: tomleslie 13876

October 27 2021

0 0

Below is an uploaded worksheet, based on your original question. (upload using the big green up-arrow in the Mapleprimes toolbar

Download upl.mw

However this (and your original question) contains the function F1() which you have not defined - so no-one here can do much with the information you provide

The only reference you give is to an academic paper behind a paywall - realsitically do you think I'm going to pay to read this!?

Looks(?) like a version issue...

Answered: tomleslie 13876

October 22 2021

0 0

@dearcia
I have checked my original code all the way back to Maple 18 (released sometime in 2014) and it works

Which Maple version are you using?

Download the attached: do nothing except hit the !!! icon in the Maple toolbar, save the results and upload them here using the big green up-arrow in the Mapleprimes toolbar. That way I can see exactly what your particular Maple installation is doing with my code

dplt2.mw

Well...

Answered: tomleslie 13876

October 20 2021

0 0

@eslamelidy

Once I fix a few typos (like the difference between epsilon and varepsilon!!), then the attached worksheet will produce the attached Excel file.

General advice - when exporting to Excel, it is usualy better if the data is organised as a Matris or a 2D table

In the attached worksheet you will have to change to filepath in the ExcelTools:-Export() command to something appropriate for your installation

XT.mw

data.xlsx

Then...

Answered: tomleslie 13876

October 18 2021

0 0

@Zeineb

why don't you show a worksheet where you do it?

Observation...

Answered: tomleslie 13876

October 17 2021

0 0

@Preben Alsholm
you state

Obviously the real value is wrong since it must be larger than -2

\Well the value obtained is 'infinity' - which (the last time I checked) is larger than -2

Shorter...

Answered: tomleslie 13876

October 12 2021

0 0

@JAMET

would be the code in the attached, although why you want to write your own taylor() command is a mystery

Download myTayl.mw

I tend to agree with you...

Answered: tomleslie 13876

October 02 2021

0 0

@mmcdara

Adjusting the Digits setting was unnecessary in Maple2015, Maple2016, Maple2017, Maple2018, but is (apparently?) required in Maple2019, Maple2020 and Maple2021.

Why?

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These are replies submitted by tomleslie

Interesting...

Errr yes...

I don't think so...

No...

Don't understand...

The easy way...

Don't understand...

Modification...

No you didn't...

Looks(?) like a version issue...

Well...

Then...

Observation...

Shorter...

I tend to agree with you...

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