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i asked it to show explanations

and got an solution about that, but it doesnt work in my Maple

i wanna know what do i wrong , why it`s not working right

 

Dear Community Members,

 

We have problem with calculation in Maple v11 and v18. when we make a calculation by using maple v11 and v18, we was not able to get the solution as you see enclosed. when we clicked to "enter + ; ", programme does not run.

 

I currently have a function quadsum(n) that determines the [x,y] solutions of the above equation for an integer n. :

quadsum:= proc(n::nonnegint)
local
k:= 0, mylist:= table(),
x:= isqrt(iquo(n,2)), y:= x, x2:= x^2, y2:= y^2;
if 2*x2 <> n then x:= x+1; x2:= x2+2*x-1; y:= x; y2:= x2; end if;
while x2 <= n do
y:= isqrt(n-x2); y2:= y^2;
if x2+y2 = n then k:= k+1; mylist[k]:= [x,y] end if;
x:= x+1; x2:= x2+2*x-1;
end do;
convert(mylist, list)
end proc:

How would I alter this so that I get [x,y] for n= (5^a).(13^b).(17^c)(29^d) for non-negative integers a,b,c,d?

please is there any one can help me to find a solution of a sytem of 3 non linear equations each with 3 variable and with more than 30 unknown coefficients

this is the system

solve({EEE_x(x, y, z) = 0, EEE_y(x, y, z) = 0, EEE_z(x, y, z) = 0}, {x, y, z})

where x,y,r are the unknowns

and the three equations are simply the partial derivative with respect to x,y and z repectively

EEE_x(x,y,z):=(&DifferentialD;)/(&DifferentialD; x) EE(x,y,z)

EEE_y(x,y,z):=(&DifferentialD;)/(&DifferentialD; y) EE(x,y,z)

EEE_z(x,y,z):=(&DifferentialD;)/(&DifferentialD;z)EE(x,y,z)

the main equation is EE where (it has 3 variables and more than 30 qunknowns coefficients

(x, y, z) ->

1
----------------------------------------------------------------
2
/ 2 2 2\
hh \ii + jj x + ll z + mm y + 100. y + nn y z + oo x + pp z /

/ 2 2 2 2 3 2
\p z y + q z y + l z x + g z x + o z y + n z x + m y x

2 2 2 3 2 2 2
+ j y x + k y x + i z y + d z y + f z x + h z y

2 2 4 3 2 3
+ e y x + u z y x + v z y x + a + b x + c x + r x + s z

2 2 4 3 4 \
+ t z + bb z + cc y + dd y + ee y + ff y + gg z + aa x/

 

I'm trying to solve some ODE analitically. But Maple gives me an incorrect solution. What am I doing wrong? Thank you.

 

Dear All,

i am solving a system of pde with boundar conditons then i got this error...

Error, (in pdsolve/numeric/plot) unable to compute solution for tau>HFloat(0.0):

Thank.

jeffrey_fluid.mw

restart

with(plots):

``

Pr := .71;

.71

 

1

 

1

 

1

(1)

PDE := {(diff(theta(eta, tau), eta, eta))/Pr+f(eta, tau)*(diff(theta(eta, tau), eta))-theta(eta, tau)*(diff(f(eta, tau), eta))-a*(diff(theta(eta, tau), tau)) = 0, diff(f(eta, tau), eta, eta, eta)+f(eta, tau)*(diff(f(eta, tau), eta, eta))-(diff(f(eta, tau), eta))^2-a*(diff(f(eta, tau), eta, tau))-K*(a*(diff(f(eta, tau), eta, eta, eta, tau))+2*(diff(f(eta, tau), eta))*(diff(f(eta, tau), eta, eta, eta))-(diff(f(eta, tau), eta, eta))^2-f(eta, tau)*(diff(f(eta, tau), eta, eta, eta, eta)))+lambda*(1+epsilon*cos(Pi*tau))*theta(eta, tau) = 0};

{1.408450704*(diff(diff(theta(eta, tau), eta), eta))+f(eta, tau)*(diff(theta(eta, tau), eta))-theta(eta, tau)*(diff(f(eta, tau), eta))-(diff(theta(eta, tau), tau)) = 0, diff(diff(diff(f(eta, tau), eta), eta), eta)+f(eta, tau)*(diff(diff(f(eta, tau), eta), eta))-(diff(f(eta, tau), eta))^2-(diff(diff(f(eta, tau), eta), tau))-K*(diff(diff(diff(diff(f(eta, tau), eta), eta), eta), tau)+2*(diff(f(eta, tau), eta))*(diff(diff(diff(f(eta, tau), eta), eta), eta))-(diff(diff(f(eta, tau), eta), eta))^2-f(eta, tau)*(diff(diff(diff(diff(f(eta, tau), eta), eta), eta), eta)))+(1+cos(Pi*tau))*theta(eta, tau) = 0}

(2)

IBC := {f(0, tau) = 0, f(10, tau) = 0, f(eta, 0) = 0, theta(0, tau) = 1, theta(10, tau) = 0, theta(eta, 0) = 0, (D[1](f))(0, tau) = 1, (D[1](f))(10, tau) = 0};

{f(0, tau) = 0, f(10, tau) = 0, f(eta, 0) = 0, theta(0, tau) = 1, theta(10, tau) = 0, theta(eta, 0) = 0, (D[1](f))(0, tau) = 1, (D[1](f))(10, tau) = 0}

(3)

L := [1]

[1]

(4)

for i to 1 do K := L[i]; pds := pdsolve(PDE, IBC, numeric, spacestep = 1/100); p[i] := plots[display]([seq(pds:-plot(f, tau = 1, eta = 0 .. 1, legend = L[i]), j = 5)]) end do

1

 

module () local INFO; export plot, plot3d, animate, value, settings; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; end module

 

Error, (in pdsolve/numeric/plot) unable to compute solution for tau>HFloat(0.0):
Newton iteration is not converging

 

display({p[1]})

Error, (in plots:-display) expecting plot structures but received: {p[1]}

 

``

 

Download jeffrey_fluid.mw

Hi

I need your help .. I solve a system and I get the error Warning, solutions may have been lost.

The maple code is attached.

testerror.mw

Thank you for your help.

 

Dear all:

hello everybody;

I need your help to solve the system f(x,y)=0, and g(x,y)=0, such that there some parameter in the system, also all the parameter are positive and also our unkowns  x and y are also positive.

I try to write this code. I feel that under some condition we can have four solution or three or two. I need your help. Many thinks.

 

Systemsolve.mw

Hello all,

I have the following equation:

N*exp(-(1/2)*eta*epsilon*(N*alpha*epsilon*w+2*N*w*C[max]-alpha*epsilon*z-2*Q1*alpha)/(w*N))*S1*upsilon*w-N*S1*upsilon*w+K1^2*alpha*eta*z*epsilon+K1*alpha*eta*z*epsilon*S1 = 0

in which I need to find solution for epsilon (analytical solution) when epsilon>0.  

Thanks,

Dmitry

 

I have the following system of non-linear equations and want to find their solutions experimenting with my parameters. I also want to restrict the solutions to be non-negative. I have done the following, but i am sure it exist a more efficient way. Can somone help on this? 

 

eqns := [A = (gr_c+delta)*kh^(1-alpha)/sav_rate, theta = Rk*(Rh-Rk)/(gamma*((Rh-Rk)^2+sigma^2)), theta = 1*1+kh, Rk = 1+rk-delta, Rh = 1+rh-delta, rk = A*alpha*kh^(alpha-1), rh = A*(1-alpha)*kh^alpha, sigma = sigmay/theta, varrho = Rap^((eps-1)*eps/(1-gamma)), Rap = Rk^(1-gamma)+(1-gamma)*Rk^(-gamma)*theta*(Rh-Rk)-.5*Rk^(-gamma-1)*gamma*(1-gamma)*theta^2*((Rh-Rk)^2+sigma^2), R = Rk+theta*(Rh-Rk), beta = ((1+gr_c)/R)^(1/eps)/varrho];
print(`output redirected...`); # input placeholder
[
[
[
[
[ (1 - alpha)
[ (gr_c + delta) kh
[A = ----------------------------,
[ sav_rate
[

Rk (Rh - Rk)
theta = ---------------------------, theta = 1 + kh,
/ 2 2\
gamma \(Rh - Rk) + sigma /

Rk = 1 + rk - delta, Rh = 1 + rh - delta,

(alpha - 1) alpha
rk = A alpha kh , rh = A (1 - alpha) kh ,

/(eps - 1) eps\
|-------------|
sigmay \ 1 - gamma /
sigma = ------, varrho = Rap , Rap =
theta

(1 - gamma) (-gamma)
Rk + (1 - gamma) Rk theta (Rh - Rk) - 0.5

(-gamma - 1) 2 / 2 2\
Rk gamma (1 - gamma) theta \(Rh - Rk) + sigma /,

/ 1 \]
|---|]
\eps/]
/1 + gr_c\ ]
|--------| ]
\ R / ]
R = Rk + theta (Rh - Rk), beta = ---------------]
varrho ]
]
vals := [alpha = .36, delta = 0.6e-1, sigmay = sqrt(0.313e-1), gamma = 3, eps = .5, gr_c = 0.2e-1, sav_rate = .23];
eval(eqns, vals);
print(`output redirected...`); # input placeholder
[
[
[
[ 0.64 Rk (Rh - Rk)
[A = 0.3478260870 kh , theta = -----------------------,
[ / 2 2\
[ 3 \(Rh - Rk) + sigma /

0.36 A
theta = 1 + kh, Rk = 0.94 + rk, Rh = 0.94 + rh, rk = ------,
0.64
kh

0.36 0.1769180601
rh = 0.64 A kh , sigma = ------------,
theta

0.1250000000
varrho = Rap ,

1 2 theta (Rh - Rk)
Rap = --- - -----------------
2 3
Rk Rk

2 / 2 2\
3.0 theta \(Rh - Rk) + sigma /
+ --------------------------------, R = Rk + theta (Rh - Rk),
4
Rk

2.000000000]
/1\ ]
1.0404 |-| ]
\R/ ]
beta = ---------------------]
varrho ]
]
eqns := [A = .3478260870*kh^.64, theta = (1/3)*Rk*(Rh-Rk)/((Rh-Rk)^2+sigma^2), theta = 1+kh, Rk = .94+rk, Rh = .94+rh, rk = .36*A/kh^.64, rh = .64*A*kh^.36, sigma = .1769180601/theta, varrho = Rap^.1250000000, Rap = 1/Rk^2-2*theta*(Rh-Rk)/Rk^3+3.0*theta^2*((Rh-Rk)^2+sigma^2)/Rk^4, R = Rk+theta*(Rh-Rk), beta = 1.0404*(1/R)^2.000000000/varrho];
print(`output redirected...`); # input placeholder
[
[
[
[ 0.64 Rk (Rh - Rk)
[A = 0.3478260870 kh , theta = -----------------------,
[ / 2 2\
[ 3 \(Rh - Rk) + sigma /

0.36 A
theta = 1 + kh, Rk = 0.94 + rk, Rh = 0.94 + rh, rk = ------,
0.64
kh

0.36 0.1769180601
rh = 0.64 A kh , sigma = ------------,
theta

0.1250000000
varrho = Rap ,

1 2 theta (Rh - Rk)
Rap = --- - -----------------
2 3
Rk Rk

2 / 2 2\
3.0 theta \(Rh - Rk) + sigma /
+ --------------------------------, R = Rk + theta (Rh - Rk),
4
Rk

2.000000000]
/1\ ]
1.0404 |-| ]
\R/ ]
beta = ---------------------]
varrho ]
]

solve(eqns, [Rk, Rh, varrho, Rap, beta, R, A, sigma, theta, rk, rh, kh]);

Hello I am a Maple 15 user and I am using the command fsolve to solve for the intersection of two curves over a specified interval in x, namely from 0 to the lim defined in the Maple document. The specified interval contains asymptotes and when I specify the full interval only one of the three solutions is returned even if I can see that there are three distinct solutions by looking at the plot of RHS and LHS. Should I use another technique to find the solution or is my implementation of fsolve command wrong?

Thanks in advance


restart

with(ListTools):

n1 := 1:

n2 := 1.50:

n3 := 1.40:

lambda := 1.3:

k0 := 2*Pi/lambda:

d := 3:

x0 := k0*d:

arg1 := sqrt(x0^2*(n2^2-n1^2)):

arg2 := sqrt(x0^2*(n2^2-n3^2)):

lim := FindMinimalElement([arg1, arg2]):

sqr1 := sqrt(x0^2*(n2^2-n1^2)-x^2):

sqr2 := sqrt(x0^2*(n2^2-n3^2)-x^2):

LHS := tan(x):

RHS := (sqr1+sqr2)/(x*(1-sqr1*sqr2/x^2)):

plot([LHS, RHS], x = 0 .. lim, y = -6 .. 6)

 

fsolve(RHS = LHS, x = (1/2)*Pi .. 3*Pi*(1/2))

2.634254816

(1)

fsolve(RHS = LHS, x = 3*Pi*(1/2) .. 9*Pi*(1/4))

5.222527128

(2)

fsolve(RHS = LHS, x = 9*Pi*(1/4) .. lim)

7.598486053

(3)

``


Download HW4Q2.mw

Hello,

I have been trying to compute the analytical solution of two dimensional diffusion equation with zero neumann boundary conditions (no-flux) in polar coordinates using the solution in Andrei Polyanin's book. When I use 2d Gaussian function as initial condition, i cannot get the result. If I use some nicer function like f(r,phi)=1-r; there is no problem.  

Any idea why this happens? or any suggestion to compute the analytical solution?

Thanks!

HB 

M := Matrix([[3.83170597020751, 7.01558666981561, 10.1734681350627, 13.3236919363142, 16.4706300508776], [1.84118378134065, 5.33144277352503, 8.53631636634628, 11.7060049025920, 14.8635886339090], [3.05423692822714, 6.70613319415845, 9.96946782308759, 13.1703708560161, 16.3475223183217], [4.20118894121052, 8.01523659837595, 11.3459243107430, 14.5858482861670, 17.7887478660664], [5.31755312608399, 9.28239628524161, 12.6819084426388, 15.9641070377315, 19.1960288000489], [6.41561637570024, 10.5198608737723, 13.9871886301403, 17.3128424878846, 20.5755145213868], [7.50126614468414, 11.7349359530427, 15.2681814610978, 18.6374430096662, 21.9317150178022], [8.57783648971407, 12.9323862370895, 16.5293658843669, 19.9418533665273, 23.2680529264575], [9.64742165199721, 14.1155189078946, 17.7740123669152, 21.2290626228531, 24.5871974863176], [10.7114339706999, 15.2867376673329, 19.0045935379460, 22.5013987267772, 25.8912772768391], [11.7708766749555, 16.4478527484865, 20.2230314126817, 23.7607158603274, 27.1820215271905]]):

c := 10:

A := 5:

w := proc (r, phi, t) options operator, arrow; int(int(f(xi, eta)*G(r, phi, xi, eta, t)*xi, xi = 0 .. 5), eta = 0 .. 2*Pi) end proc:

with(plots):

Warning,  computation interrupted

 

``



Download 2d_soln.mw

Having solution of an inequations system, is there a way/function/algorithm to find a particular numeric solution (as simplex[minimize] can do) ?

ex:

Q := {1 < x - y, x + y < 1};

R := solve(Q);

      { x < 1 - y, y < 0, y + 1 < x }

manually it's easy to find some numeric solutions:


      y = -1, x = 1
      y = -2, x = 0

but I need an automatic way.

Thank you for your help
s.py

 

Dear Maple enthusiasts,

I am unable to find a working method to solve a system of 8 equations, of which 4 are differential equations. The system contains 8 unknown variables and the goal is to find an expression for each of these variables as a function of the time t. I have attached the code of my project at the bottom of this message.

I have tried the following:

  1. Using solve/dsolve to solve all 8 equations at once. This results in Maple eating up all of my memory and never finishing its calculations.
  2. First using solve to solve the 4 non-differential equations so that I get 4 out of 8 variables as a function of the 4 remaining variables. This results in an expression containing RootOf() for each of the 4 veriables I'm solving for, which prevents me from using these expressions in the 4 remaining differential equations.
  3. First using dsolve to solve the differential equations, which gives once again an expression for 4 variables as a function of the 4 remaining variables. I then use solve to solve the 4 remaining equations with the new found expressions. This results in an extremely long solution for each of the variables.

The code below contains the 3rd option I tried.

Any help or suggestions would be greatly appreciated. I have been scratching my head so much that I'm getting bald and whatever I search for on google or in the Maple help, I can't find a good reference to a system of differential equations together with other equations.

 

 

restart:

PARK - Mixed control

 

 

Input parameters

 

 

Projected interface area (m²)

A_int:=0.025^2*Pi:

 

Temperature of the process (K)

T_proc:=1873:

 

Densities (kg/m³)

Rho_m:=7000: metal

Rho_s:=2850: slag

 

Masses (kg)

W_m:=0.5: metal

W_s:=0.075: slag

 

Mass transfer coefficients (m/s)

m_Al:=3*10^(-4):

m_Si:=3*10^(-4):

m_SiO2:=3*10^(-5):

m_Al2O3:=3*10^(-5):

 

Weight percentages in bulk at t=0 (%)

Pct_Al_b0:=0.3:

Pct_Si_b0:=0:

Pct_SiO2_b0:=5:

Pct_Al2O3_b0:=50:

 

Weight percentages in bulk at equilibrium (%)

Pct_Al_beq:=0.132:

Pct_Si_beq:=0.131:

Pct_SiO2_beq:=3.13:

Pct_Al2O3_beq:=52.12:

 

Weight percentages at the interface (%)

Constants

 

 

Atomic weights (g/mol)

AW_Al:=26.9815385:

AW_Si:=28.085:

AW_O:=15.999:

AW_Mg:=24.305:

AW_Ca:=40.078:

 

Molecular weights (g/mol)

MW_SiO2:=AW_Si+2*AW_O:

MW_Al2O3:=2*AW_Al+3*AW_O:

MW_MgO:=AW_Mg+AW_O:

MW_CaO:=AW_Ca+AW_O:

 

Gas constant (m³*Pa/[K*mol])

R_cst:=8.3144621:

 

Variables

 

 

with(PDEtools):
declare((Pct_Al_b(t),Pct_Al_i(t),Pct_Si_b(t),Pct_Si_i(t),Pct_SiO2_b(t),Pct_SiO2_i(t),Pct_Al2O3_b(t),Pct_Al2O3_i(t))(t),prime=t):

Equations

 

4 rate equations

 

 

Rate_eq1:=diff(Pct_Al_b(t),t)=-A_int*Rho_m*m_Al/W_m*(Pct_Al_b(t)-Pct_Al_i(t));

 

Rate_eq2:=diff(Pct_Si_b(t),t)=-A_int*Rho_m*m_Si/W_m*(Pct_Si_b(t)-Pct_Si_i(t));

 

Rate_eq3:=diff(Pct_SiO2_b(t),t)=-A_int*Rho_s*m_SiO2/W_s*(Pct_SiO2_b(t)-Pct_SiO2_i(t));

 

Rate_eq4:=diff(Pct_Al2O3_b(t),t)=-A_int*Rho_s*m_Al2O3/W_s*(Pct_Al2O3_b(t)-Pct_Al2O3_i(t));

 

3 mass balance equations

 

 

Mass_eq1:=0=(Pct_Al_b(t)-Pct_Al_i(t))+4*AW_Al/(3*AW_Si)*(Pct_Si_b(t)-Pct_Si_i(t));

 

Mass_eq2:=0=(Pct_Al_b(t)-Pct_Al_i(t))+4*Rho_s*m_SiO2*W_m*AW_Al/(3*Rho_m*m_Al*W_s*MW_SiO2)*(Pct_SiO2_b(t)-Pct_SiO2_i(t));

 

Mass_eq3:=0=(Pct_Al_b(t)-Pct_Al_i(t))+2*Rho_s*m_Al2O3*W_m*AW_Al/(Rho_m*m_Al*W_s*MW_Al2O3)*(Pct_Al2O3_b(t)-Pct_Al2O3_i(t));

 

1 local equilibrium equation

 

 

Gibbs free energy of the reaction when all of the reactants and products are in their standard states (J/mol). Al and Si activities are in 1 wt pct standard state in liquid Fe. SiO2 and Al2O3 activities are in respect to pure solid state.

 

delta_G0:=-720680+133*T_proc:

 

Expression of mole fractions as a function of weight percentages (whereby MgO is not taken into account, but instead replaced by CaO ?)

x_Al2O3_i(t):=(Pct_Al2O3_i(t)/MW_Al2O3)/(Pct_Al2O3_i(t)/MW_Al2O3 + Pct_SiO2_i(t)/MW_SiO2 + (100-Pct_SiO2_i(t)-Pct_Al2O3_i(t))/MW_CaO);
x_SiO2_i(t):=(Pct_SiO2_i(t)/MW_SiO2)/(Pct_Al2O3_i(t)/MW_Al2O3 + Pct_SiO2_i(t)/MW_SiO2 + (100-Pct_SiO2_i(t)-Pct_Al2O3_i(t))/MW_CaO);

 

Activity coefficients

Gamma_Al_Hry:=1: because very low percentage present  during the process (~Henry's law)

Gamma_Si_Hry:=1: because very low percentage present  during the process (~Henry's law)

Gamma_Al2O3_Ra:=1: temporary value!

Gamma_SiO2_Ra:=10^(-4.85279678314968+0.457486603678622*Pct_SiO2_b(t)); very small activity coefficient?
plot(10^(-4.85279678314968+0.457486603678622*Pct_SiO2_b),Pct_SiO2_b=3..7);

 

Activities of components

a_Al_Hry:=Gamma_Al_Hry*Pct_Al_i(t);
a_Si_Hry:=Gamma_Si_Hry*Pct_Si_i(t);
a_Al2O3_Ra:=Gamma_Al2O3_Ra*x_Al2O3_i(t);
a_SiO2_Ra:=Gamma_SiO2_Ra*x_SiO2_i(t);

 

Expressions for the equilibrium constant K

K_cst:=exp(-delta_G0/(R_cst*T_proc));

Equil_eq:=0=K_cst*a_Al_Hry^4*a_SiO2_Ra^3-a_Si_Hry^3*a_Al2O3_Ra^2;

 

Output

 

 

with(ListTools):
dsys:=Rate_eq1,Rate_eq2,Rate_eq3,Rate_eq4:
dvars:={Pct_Al2O3_b(t),Pct_SiO2_b(t),Pct_Al_b(t),Pct_Si_b(t)}:
dconds:=Pct_Al2O3_b(0)=Pct_Al2O3_b0,Pct_SiO2_b(0)=Pct_SiO2_b0,Pct_Si_b(0)=Pct_Si_b0,Pct_Al_b(0)=Pct_Al_b0:
dsol:=dsolve({dsys,dconds},dvars):

Pct_Al2O3_b(t):=rhs(select(has,dsol,Pct_Al2O3_b)[1]);
Pct_Al_b(t):=rhs(select(has,dsol,Pct_Al_b)[1]);
Pct_SiO2_b(t):=rhs(select(has,dsol,Pct_SiO2_b)[1]);
Pct_Si_b(t):=rhs(select(has,dsol,Pct_Si_b)[1]);

sys:={Equil_eq,Mass_eq1,Mass_eq2,Mass_eq3}:
vars:={Pct_Al2O3_i(t),Pct_SiO2_i(t),Pct_Al_i(t),Pct_Si_i(t)}:
sol:=solve(sys,vars);

,


Download Park_-_mixed_control_model.mw

Hi, those who are in mapleprimes.

 

i have a problem in solving inequality with symbolic notated parameters.

I wrote the following code to solve for n(SPH), but couldn't obtain any result but an error message.

solve(-s*(-n(SPF)*tau+n(SPH))/(tau-1) <= n(SPH),n(SPH)) assuming (tau<1,s>0,s<1,tau>0);

 

The error was

Error, (in assuming) when calling 'unknown'. Received: 'invalid input: Utilities:-SetSolutions expects its 2nd argument, solutions, to be of type ({list, set})({piecewise, ({list, set})({name, relation})}), but received [s = -tau~+1, [SPF = SPF, s = s, tau~ <= 0]]'

 

Please tell me how I should do to solve the inequality.

 

Thanks in advance.

 

taro

 

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