Items tagged with ode ode Tagged Items Feed

g[1] := (diff(a(t), t))/(t^2-1) = 1;
g[2] := (diff(a(t), t))*(diff(b(t), t)) = 1;
dsolve({eq2, eq3});
with(DynamicSystems):
sys := DiffEquation([g[1]=1, g[2]=1], inputvariable = [b(t)], outputvariable = [a(t), b(t)]):
ts := 0.1:
t_sim := 10.0:
#in_t := Sine(1, 1, 0, 0):
#in_z := Sine(1, 1, 0, 0, samplecount = round(t_sim/ts), sampletime = ts, discrete):
in_t := t:
sol := Simulate(sys, [in_t]):
p1 := plots[odeplot](sol, [[t, a(t)]], t = 0 .. t_sim, numpoints = 200, color = red):
Error, (in DEtools/convertsys) unable to convert to an explicit first-order system
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

Can Maple simplify these DE's by eliminating the d/dt VL(t) by taking the derrivative of the bottom equation and substituting in the first one? 

So im trying to solve multiple ODES using dsolve(numeric) but I jsut cant get it to work.

I kep getting this one error: 

Error, (in f) unable to store '-HFloat(0.020918994979034728)-HFloat(0.09184018333019917)*I' when datatype=float[8]

 

This is my uploaded file 

(for some reason the uploaded file didnt show the error at the bottom so i just pasted it in the spot it would appear.

Download CHE504_HW5.mw

Given:

restart

dt := 2.07*0.254e-1

0.52578e-1

(1)

dto := 2.38*0.254e-1

0.60452e-1

(2)

ho := 5000

5000

(3)

``

Ltube := 5

5

(4)

``

Po := 2.5

2.5

(5)

To := 350

350

(6)

dp := 0.3e-2

0.3e-2

(7)

tau := 3

3

(8)

dpore := 5.2*10^(-9)

0.5200000000e-8

(9)

kfluid := 0.485e-1

0.485e-1

(10)

ksolid := 1.67

1.67

(11)

kpipe := 17

17

(12)

Cpair := 1.01

1.01

(13)

`μ_air` := 3.16*10^(-5)

0.3160000000e-4

(14)

rho := P(z)*(28.9*(1/1000))/(Rgas*(T(z)+273.15))

0.2890000000e-1*P(z)/(Rgas*(T(z)+273.15))

(15)

``

Rgas := 8.2057*10^(-5)

0.8205700000e-4

(16)

``

``

density calculation n/v = (P/RT)*mw_air, kg/m^3

``

`ρi` := (2.5*28.966)/(0.82057e-1*(350+273.15))

1.416186012

(17)

NULL

Volumetric flow, m^3/s

((1/60)*((1/300)*((1/1000)*(180*1000000)*.4535)*(1/24))*(1/60))/(1.416)

0.2224085844e-2

(18)

``

NULL

Superficial velocity, m/s

NULL

Vsi := evalf(%/((1/4)*Pi*(2.07*0.254e-1)^2))

1.024362190

(19)

Gs constant, kg/m^2-s

Error, missing operator or `;`

 

Gsi := `ρi`*Vsi

1.450687405

(20)

Gs := 1.45

1.45

(21)

``

``

NULL

Void fraction, epsilon,b

`εb` := .38+0.73e-1*(1+(0.525e-1/(0.3e-2)-2)^2/(0.525e-1/(0.3e-2))^2)

.5102677551

(22)

hi

hi := 3.6*kfluid*(dp*Gs/(`μ_air`*`εb`))^.365/dp

448.9928888

(23)

kinetic parameter

K := ln(19.837-13636/(T(z)+273.15))

ln(19.837-13636/(T(z)+273.15))

(24)

radial disperssion Coeff

Dr := Vs*dp/(9*(1+19.4*(dp/dt)^2))

0.3135309899e-3*Vs

(25)

thermal conductivity calculations

Kbs := kfluid*(`εb`+(1-`εb`)/(2/3*(1+kfluid/ksolid)))

0.5937050269e-1

(26)

``

Kbd := `εb`*Cpair*Gs*dp/(9*(1+19.4*(dp/dt)^2))

0.2342976727e-3

(27)

KB := Kbs+Kbd

0.5960480036e-1

(28)

Heat of reaction (deltaH), Find heat of formation for each reactant and product--> dHrxn = heat of formation(product)-heat of formation(reactant)

Error, missing operator or `;`

 

heat of formation = A + B*T + C*T^2

Hfacrolein := -7.076*10+(-5.59*10^(-2))*(273.15+350)+3.86*10^(-5)*(273.15+350)^2

-90.60509039

(29)

Hfwater := -238.41-0.122e-1*(350+273.15)+2.76*10^(-6)*(273.15+350)^2

-244.9406781

(30)

Hfpropylene := 3.62*10+(-6.49*10^(-2))*(273.15+350)+3.049*10^(-5)*(273.15+350)^2

7.59731748

(31)

`ΔHrxn` := Hfacrolein-Hfwater-Hfpropylene

146.7382702

(32)

Solving nodified Ergun Equation

f := (1-`εb`)*(1.75+(150*(1-`εb`))*`μ_air`/(dp*Gs))/`εb`

2.191735176

(33)

``

Determining U of the wall and Ueffective

``

``

Uwall := 1/(1/hi+ln(dto/dt)/(2*ksolid)+1/ho)

22.61972270

(34)

``

Ueff := 1/(1/Uwall+(1/2)*dt/(4*KB))

6.473624190

(35)

ode1 := Gs*(diff(Cprop(z), z))/rho = -K*Cprop(z)

0.4117046714e-2*(T(z)+273.15)*(diff(Cprop(z), z))/P(z) = -ln(19.837-13636/(T(z)+273.15))*Cprop(z)

(36)

ode2 := Gs*Cpair*(diff(T(z), z)) = -K*Cprop(z)*`ΔHrxn`-4*Ueff*(T(z)-350)/dt

1.4645*(diff(T(z), z)) = -146.7382702*ln(19.837-13636/(T(z)+273.15))*Cprop(z)-492.4968000*T(z)+172373.8800

(37)

ode3 := diff(P(z), z) = -f*Gs^2/(rho*dp)

diff(P(z), z) = -4.361346783*(T(z)+273.15)/P(z)

(38)

Ics1 := Cprop(0) = 0.3e-1

Cprop(0) = 0.3e-1

(39)

Ics2 := T(0) = 350

T(0) = 350

(40)

Ics3 := P(0) = 2.5

P(0) = 2.5

(41)

NULL

dsolve({Ics1, Ics2, Ics3, ode1, ode2, ode3}, {Cprop(z), P(z), T(z)})

Error, (in f) unable to store '-HFloat(0.020918994979034728)-HFloat(0.09184018333019917)*I' when datatype=float[8]

 

 

NULL

NULL

``

hi all

 

i have tow equations and i want plot q vs.A , that A change beetwin 0..phi. vn and a are definite and positive.

plz plz help me

 

(diff(f,y))^2-(f[y]^4)/4+q^2/(f[y]^2)+(1+2*q^2)*(f[y]^2)/2=piecewise(y<-a,1/4+2*q^2,-a<y<a,vn*(f[y]^2)-vn+1/4+2*q^2,y>a,1/4+2*q^2);

phiB[infinity]=q*int(f,y=-infinity..infinity):
A:=phiB[infinity]:

 

 

 

Hi everyone!

I tried to plot the solution of the following ode, but I only got the message error:

Warning, cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up

(file attached)

Problem.mw

https://dl.dropboxusercontent.com/u/66502600/Problem.mw

 

Please, help me!

 

Thank you so much!

 



thanks. I played around, and had problems implementing your ideas for one of the systems I'm interested in.I don't see a difference between this and what you had advised me on, but it gets an error.

any idea why?
or how to fix it?

thing1 := diff(B[1](t), t) = piecewise(t <= 500, 0.3e-2-(63/10000)*B[1](t)-(3/500)*B[2](t), -(3/10000)*B[1](t)):
thing2 := diff(B[1](t), t) = piecewise(t <= 500, 0.1e-1-(1/50)*B[1](t)-(13/625)*B[2](t), -(1/1250)*B[2](t)):
sol := dsolve({thing1, thing2, B[1](0) = 0, B[2](0) = 0}, {B[1](t), B[2](t)}, numeric, output = listprocedure); plots:-odeplot(sol, [B[1](t), B[2](t)], t = 450 .. 550);

Error, (in dsolve/numeric/DAE/explicit) unable to obtain the standard form of the DAE system due to the presence of leading dependent variables/derivatives in the piecewise: piecewise(t <= 500, 1/100-(1/50)*B[1](t)-(13/625)*B[2](t), -(1/1250)*B[2](t))-piecewise(t <= 500, 3/1000-(63/10000)*B[1](t)-(3/500)*B[2](t), -(3/10000)*B[1](t))
Error, (in plots/odeplot) curve is not fully specified in terms of the ODE solution, found additional unknowns {B[1](t), B[2](t)}


Hello

I have an SEIR model.

Equation 5 is for disease death but I would like to plot the cumulative numbers of disease death which will be the integral of Equation 5. I added the integral inside odeplot but it is not working. Any idea  about  how to compute the integral ?

Maple code is attached

Thank you

code.mw

PLEASE..!! CAN ANYONE HELP ME IN CODING ON MAPPLE 13 TO CHANGE PDE INTO ODE??

MY FUNCTION IS THIS

U[t, t]-U[t, t, x, x]-(aU[]-b*U[]^3)[x, x] = 0

Hi,

 

I have an issue calculating an electronics circuit with Maple, using units. I have a current source that I know, and I want to determin the voltage in a capacitor by solving an ODE (except that the current source is defined piecewise). And to make sure I have all the units and scales right, I use the standard unit package. All my variables have their units defined.

Except that Maple doesn't want to solve the equation. It seems to me that it assumes that the function I am trying to solve is unitless, and therefore refuses to solve. 

V__out := 3*Unit('kV');

C__out := 2*Unit('nF');
R__blead := 520*Unit('`k&Omega;`');

I__fly := proc (t) options operator, arrow; Unit('A')*piecewise(t < 3.25*Unit('us'), (1+(-1)*t/(3.25*Unit('us')))*.2, 0) end proc;

 

dsolve({I__fly(t*Unit('s'))-V__C(t*Unit('s'))/R__blead = C__out*(diff(V__C(t*Unit('s')), t)), V__C(0*Unit('s')) = V__out}, V__C(t*Unit('s')));
Error, (in Units:-Standard:-+) the units `A` and `S` have incompatible dimensions

 

Is there a way to make Maple assume the unit of what it's trying to solve ? I need it to understands that V__C is in Unit('V') ...

 

Thanks

 

See attached file and code

0. This is the differential equation I'm trying to do:

http://www.intmath.com/differential-equations/6-rc-circuits.php

https://i.imgur.com/zlVIisR.png

 

1. After you look at the above imgur link, could you help me with this error 

Error, (in Units:-Standard:-+) the units ``&Omega;`` and `1/F` have incompatible dimensions

  

2. Why does my solve ODE fail? 

 

See my code: 

test_maple.mw

using FDM or FEM rather than dsolve?

ode.docxode.docx

Hi, Im now trying to run my code. But it took like years to even getting the results. may I know any solutions on how to get faster results? Because I have run this code for almost 4 hours yet there is still 'Evaluating...' at the corner left. And when I tried to stop the program, it will stop at 'R1...'.

 

Digits := 18;
with(plots):n:=1.4: mu(eta):=(diff(U(eta),eta)^(2)+diff(V(eta),eta)^(2))^((n-1)/(2)):
Eqn1 := 2*U(eta)+(1-n)*eta*(diff(U(eta), eta))/(n+1)+diff(W(eta), eta) = 0;
Eqn2 := U(eta)^2-(V(eta)+1)^2+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(U(eta), eta))-mu(eta)*(diff(U(eta), eta, eta))-(diff(U(eta), eta))*(diff(mu(eta), eta)) = 0;
Eqn3 := 2*U(eta)*(V(eta)+1)+(W(eta)+(1-n)*eta*U(eta)/(n+1))*(diff(V(eta), eta))-mu(eta)*(diff(V(eta), eta, eta))-(diff(V(eta), eta))*(diff(mu(eta), eta)) = 0;
bcs1 := U(0) = 0, V(0) = 0, W(0) = 0;
bcs2 := U(4) = 0, V(4) = -1;
R1 := dsolve({Eqn1, Eqn2, Eqn3, bcs1, bcs2}, {U(eta), V(eta), W(eta)}, initmesh = 30000, output = listprocedure, numeric);
Warning, computation interrupted
for l from 0 by 2 to 4 do R1(l) end do;
plot1 := odeplot(R1, [eta, U(eta)], 0 .. 4, numpoints = 2000, color = red);

 

Thankyou in advance :)

how can i improve doing the graph with various parameter

do anyone have abother numerical method in maple rather than rk45 felhberg

like keller box/homotopy/ or anything

i have attchassignment.mwsassignment.pdf

restart

with(plots)

%?

Eq1 := diff(f(eta), `$`(eta, 3))+(diff(f(eta), `$`(eta, 2)))*f(eta)-(diff(f(eta), eta))^2+4 = 0

diff(diff(diff(f(eta), eta), eta), eta)+(diff(diff(f(eta), eta), eta))*f(eta)-(diff(f(eta), eta))^2+4 = 0

(1)

%?

Eq2 := diff(theta(eta), `$`(eta, 2))+Pr*(diff(theta(eta), eta))*f(eta) = 0

diff(diff(theta(eta), eta), eta)+Pr*(diff(theta(eta), eta))*f(eta) = 0

(2)

%?

VPr := [0.1e-1, 0.2e-1, 0.3e-1]

etainf := 27

bcs := (D(f))(0) = 0, f(0) = 0, (D(theta))(0) = -1, (D(f))(etainf) = 2, theta(etainf) = 0

(D(f))(0) = 0, f(0) = 0, (D(theta))(0) = -1, (D(f))(27) = 2, theta(27) = 0

(3)

dsys := {Eq1, Eq2, bcs}

for i to 3 do Pr := VPr[i]; dsol[i] := dsolve(dsys, numeric); print(Pr); print(dsol[i](0)) end do

0.1e-1

[eta = 0., f(eta) = HFloat(0.0), diff(f(eta), eta) = HFloat(0.0), diff(diff(f(eta), eta), eta) = HFloat(3.4862842650940435), theta(eta) = HFloat(9.305856096452466), diff(theta(eta), eta) = HFloat(-0.9999999999999998)]

0.2e-1

[eta = 0., f(eta) = HFloat(0.0), diff(f(eta), eta) = HFloat(0.0), diff(diff(f(eta), eta), eta) = HFloat(3.4862842653392216), theta(eta) = HFloat(6.7064688361073745), diff(theta(eta), eta) = HFloat(-1.0)]

0.3e-1

[eta = 0., f(eta) = HFloat(0.0), diff(f(eta), eta) = HFloat(0.0), diff(diff(f(eta), eta), eta) = HFloat(3.4862842648459234), theta(eta) = HFloat(5.552583608770695), diff(theta(eta), eta) = HFloat(-0.9999999999999998)]

(4)

SDf1 := odeplot(dsol[1], [eta, f(eta)], 0 .. etainf, color = green, axes = box); SDf2 := odeplot(dsol[2], [eta, f(eta)], 0 .. etainf, color = red); SDf3 := odeplot(dsol[3], [eta, f(eta)], 0 .. etainf, color = blue)

display([SDf1, SDf2, SDf3], labels = ["&eta;", "f (&eta;)"], labeldirections = [horizontal, vertical], labelfont = [italic, 16, bold], axes = boxed, axesfont = [times, 14], thickness = 3)
%?

 

%?

SDfd1 := odeplot(dsol[1], [eta, diff(f(eta), eta)], 0 .. etainf, color = green, axes = box); SDfd2 := odeplot(dsol[2], [eta, diff(f(eta), eta)], 0 .. etainf, color = red); SDfd3 := odeplot(dsol[3], [eta, diff(f(eta), eta)], 0 .. etainf, color = blue)

%?

display([SDfd1, SDfd2, SDfd3], labels = ["&eta;", "f  ' (&eta;)"], labeldirections = [horizontal, vertical], labelfont = [italic, 16, bold], axes = boxed, axesfont = [times, 14], thickness = 3)

 

%?

`S&theta;1` := odeplot(dsol[1], [eta, theta(eta)], 0 .. etainf, color = green, axes = box); `S&theta;2` := odeplot(dsol[2], [eta, theta(eta)], 0 .. etainf, color = red); `S&theta;3` := odeplot(dsol[3], [eta, theta(eta)], 0 .. etainf, color = black)

display([`S&theta;1`, `S&theta;2`, `S&theta;3`], labels = ["&eta;", "&theta; (&eta;)"], labeldirections = [horizontal, vertical], labelfont = [italic, 16, bold], axes = boxed, axesfont = [times, 14], thickness = 3)

 

%?

`S&theta;d1` := odeplot(dsol[1], [eta, diff(theta(eta), eta)], 0 .. etainf, color = green, axes = box); `S&theta;d2` := odeplot(dsol[2], [eta, diff(theta(eta), eta)], 0 .. etainf, color = red); `S&theta;d3` := odeplot(dsol[3], [eta, diff(theta(eta), eta)], 0 .. etainf, color = black)

display([`S&theta;d1`, `S&theta;d2`, `S&theta;d3`], labels = ["&eta;", "&theta; '(&eta;)"], labeldirections = [horizontal, vertical], labelfont = [italic, 16, bold], axes = boxed, axesfont = [times, 14], thickness = 3)

 

%?

 

 

Download assignment.mws

 

Hello Everybody,

I was trying to apply the Newton-Raphon method("Newton" in maple) for the following problem to obtain the constants (c1...cM) without success.

eq[1] := -0.0139687 c[2] - 0.0132951 c[1] = 0
eq[2] := 24806.4 c[2] - 0.0139687 c[1] = 0

If anybody has experience with it or knows how to use it I would really appreciate your help.

 

Just to introduce the previous steps of calculations leading to the problem:To calculate the critical buckling force N and the shape of a rectangular uniformly loaded plate the governing diff. equation is the following

D11*w''''(x)+(2*D12+4*D66)*w''(x)''(y)+D22*w''''(y)+N*w''(x)=0

For the follwing solution of a boundary value problem(Boundary conditions:clamped-clamped: w(x=0,x=a)=0 & w'(x=0,x=a)=0) I applied the Ritz method:

w:=sum(c[i]*(cos(2*i*Pi*x/a)-1)),i=1..M)

Thus the Potential Energy P is:

P:=16537.6*c[2]^2-0.0139687*c[2]*c[1]+1033,60*c[1]^2-9.86960*N*c[2]^2-2.46740*N*c[1]^2

 deriving P to each constant c and setting them =0 leads to:

eq[1] := -0.0139687 c[2] + 2067.20 c[1] - 4.93480 N c[1] = 0
eq[2] := 33075.2 c[2] - 0.0139687 c[1] - 19.7392 N c[2] = 0

After calculating N=418,902  and feeding eq1 and eq 2,the follwing equations if two terms are considered:

eq[1] := -0.0139687 c[2] - 0.0132951 c[1] = 0
eq[2] := 24806.4 c[2] - 0.0139687 c[1] = 0

Everything I tried resulted in any c1 = c2 = 0 which is not  realistic. Maybe I made a mistake earlier.

Thanks a lot in advance.

Sam

 Plate_Buckling.mw

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