Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

eq1 := diff(f(x), x, x, x)+(1/2)*x*cos(alpha)*(diff(f(x), x, x))+(1/2)*sin(alpha)*f(x)*(diff(f(x), x, x))+G[r]*theta(x)+G[m]*phi(x) = 0;

eq2 := diff(theta(x), x, x)+(1/2)*Pr*cos(alpha)*x*(diff(theta(x), x))+sin(alpha)*f(x)*(diff(theta(x), x))+N[b]*(diff(theta(x), x))*(diff(phi(x), x))+N[t]*(diff(theta(x), x))^2 = 0;

eq3 := diff(phi(x), x, x)+(1/2)*Le*cos(alpha)*x*(diff(phi(x), x))+sin(alpha)*f(x)*(diff(phi(x), x))+N[t]*(diff(theta(x), x, x))/N[b] = 0;

ics := f(0) = 0, (D(f))(0) = gamma*((D@@2)(f))(0), theta(0) = 1+tau*(D(theta))(0), phi(0) = 1;

bcs := (D(f))(infty) = 0, theta(infty) = 0, phi(infty) = 0;

Parameters := G[r] = 5, G[m] = 3, Pr = 7, N[b] = .1, N[t] = .1, Le = 1, gamma = .2, tau = .1, alpha = 30*degree;

I have a equation

((D@@2)(theta))(eta) = -(1/2)*(D(theta))(eta)*(-2*(D(phi))(eta)*beta*epsilon*lambda*D[B]+2*(D(phi))(eta)*beta*epsilon*mu*D[B]+f(eta)*sin(alpha)*beta*nu+2*(D(theta))(eta)*gamma*epsilon*D[t]-2*(D(theta))(eta)*beta*epsilon*D[t]+cos(alpha)*beta*eta*nu)/(beta*sigma)

and a parameters expression

Pr:=nu/sigma; N[b] := epsilon*D[B](mu-lambda)/sigma; N[t] := epsilon*D[t](gamma-beta)/(gamma*sigma); Le := nu/D[B]

How can I seperate common terms and substitute this parameters and got this following expression

((D@@2)(theta))(eta) = -(1/2)*Pr*(D(theta))(eta)*eta*cos(alpha)-(1/2)*Pr*(D(theta))(eta)*sin(alpha)*f(eta)-N[b]*(D(theta))(eta)*(D(phi))(eta)-N[t]*(D(theta))(eta)

How to conver a patial differetial equation to ordinary differential equation with or without dchange?
 

restart

declare(u(x, y, t), v(x, y, t), T(x, y, t), C(x, y, t), eta(x, y, t), psi(x, y, t), f(eta), theta(eta), phi(eta));

declare(u(x, y, t), v(x, y, t), T(x, y, t), C(x, y, t), eta(x, y, t), psi(x, y, t), f(eta), theta(eta), phi(eta))

(1)

eta := proc (x, y, t) options operator, arrow; y/(nu*t+nu*x/U[w])^(1/2) end proc:

eq1 := diff(T(x, y, t), t)+u*(diff(T(x, y, t), x))+v*(diff(T(x, y, t), y))-sigma*(diff(T(x, y, t), y, y))-epsilon*D[B]*(diff(T(x, y, t), y))*(diff(C(x, y, t), y)) = 0

diff(T(x, y, t), t)+U[w]*(D(f))(y/(nu*t+nu*x/U[w])^(1/2))*(diff(T(x, y, t), x))+(-(1/2)*f(y/(nu*t+nu*x/U[w])^(1/2))*nu/(nu*t+nu*x/U[w])^(1/2)+(1/2)*(D(f))(y/(nu*t+nu*x/U[w])^(1/2))*y*nu/(nu*t+nu*x/U[w]))*(diff(T(x, y, t), y))-sigma*(diff(diff(T(x, y, t), y), y))-epsilon*D[B]*(diff(T(x, y, t), y))*(diff(C(x, y, t), y)) = 0

(2)

``


 

Download pde_to_ode.mw

i want to plot this equations for P and t for  t= 0 t0 600 seconds..can u provide me how?

time-dependent_aerodynamic_pressure.mw

restart

k := 0.1e-1;

0.1e-1

 

5

(1)

`P₀₀` := 100;

100

(2)

V := 25;

25

(3)

rho := 1;

1

 

.5

(4)

eq := diff(P(t), t) = -k*P(t)+rho*Cp*(int(V*sin(alpha), t));

diff(P(t), t) = -0.1e-1*P(t)+12.5*sin(5)*t

(5)

solution := dsolve({eq, P(0) = `P₀₀`}, P(t));

P(t) = 1250*sin(5)*t-125000*sin(5)+exp(-(1/100)*t)*(100+125000*sin(5))

(6)

``

Download time-dependent_aerodynamic_pressure.mw

restart;

eq32r:=diff(B(r),`$`(r,3))+diff(B(r),r);

diff(diff(diff(B(r), r), r), r)+diff(B(r), r)

(1)

with(PDEtools, casesplit, declare); with(DEtools, gensys):declare(b(r), prime = r);

[casesplit, declare]

 

b(r)*`will now be displayed as`*b

 

`derivatives with respect to`*r*`of functions of one variable will now be displayed with '`

(2)

eq32r;

diff(diff(diff(B(r), r), r), r)+diff(B(r), r)

(3)

latex(eq32r);

{\frac {{\rm d}^{3}}{{\rm d}{r}^{3}}}B \left( r \right) +{\frac

{\rm d}{{\rm d}r}}B \left( r \right)

 

#instead of {\frac {{\rm d}^{3}}{{\rm d}{r}^{3}}}B I want to have B''' in my latex file.

``

``

Download convert-latex.mw

Hi everybody

I have a differential equation where derivatives (for example d/dr) have been displayed by prime notation.

I want to convert this equation latex format by keeping the prime notation not d/dr.

I would appreciate it if anyone could help me.

I have attached a sample code.

Thank you

Hadi

Hello everyone! I have found this document from Maple 18 (2014) that will be very usefull for my school work, but when i copy it into Maple 2022 i get the error message, "action, does not evaluate to a module" Is there any way for me to fix this? What i have been able to read is that i have to go in and update the code, but i have absolute no idea on how to do it? 

Kind Regards Samuel 

Regressionmodeller._Skal_laves_til_maple_22_og_23.mw

could any one help  to plot this.

Here is my code.

PWS.mw

I need to make the graph i have attached match the image below.

Is there any wrong with unknown parameter i found?How to solve this.Please Help.

restart

with(PolynomialIdeals):

``

``

randomzero := proc (ListVar) local A, G, i, lm, B, f, g; option trace; A := ListVar; G := NULL; for i to nops(A) do f := A[i]^(i+1)+randpoly([op(`minus`({op(A)}, {A[i]}))], terms = 1, coeffs = rand(-4 .. -1), degree = i); G := G, f end do; print(IsZeroDimensional(`<,>`(G))); RETURN([G]) end proc:

randomzero([x, y])

{--> enter randomzero, args = [x, y]

 

[x, y]

 

"G:="

 

x^2-y-4

 

x^2-y-4

 

y^3-3*x

 

x^2-y-4, y^3-3*x

 

true

 

<-- exit randomzero (now at top level) = [x^2-y-4, y^3-3*x]}

 

[x^2-y-4, y^3-3*x]

(1)

``

Download bug.mw

Hi

I think there is a bug in the "randpoly" command. please see the attached file line 7 of my procedure "randomzero". Why x^2-y-4 is created while terms=1 is considered and the outputs must contain binomial?

How to get U1,U2,..I dont know how to use this inverse transform.Please help to find the series.

CM.mw

Equilibrium._solutions.mw

I need to obtain the equilibrium solutions when infection is present as well as analyze the local asymptotic stability when infection is absent and present in the system

Hi, please can someone help on how non-dimensionalize PDEs. 

I have tried the following, but is not working:

restart:
eqn := (diff(theta(x, z, t), x))^2*(K[1]-K[3])*cos(theta(x, z, t))*sin(theta(x, z, t))+(diff(theta(x, z, t), x))*((diff(theta(x, z, t), z))*(-K[1]*cos(2*theta(x, z, t))+K[3]*cos(2*theta(x, z, t)))-(1/2)*gamma[1]*(4*sin(theta(x, z, t))^2*u(x, z, t)+2*u(x, z, t)*cos(2*theta(x, z, t))))+(diff(theta(x, z, t), z))^2*(K[3]-K[1])*cos(theta(x, z, t))*sin(theta(x, z, t))-(1/2)*gamma[1]*(diff(theta(x, z, t), z))*(4*sin(theta(x, z, t))^2*v(x, z, t)+2*v(x, z, t)*cos(2*theta(x, z, t)))+(diff(theta(x, z, t), z, x))*(-2*K[1]+2*K[3])*cos(theta(x, z, t))*sin(theta(x, z, t))-(diff(u(x, z, t), z))*((1/2)*gamma[2]*cos(2*theta(x, z, t))+(1/2)*gamma[1]*(2*sin(theta(x, z, t))^2+cos(2*theta(x, z, t))))-(diff(v(x, z, t), x))*((1/2)*gamma[2]*cos(2*theta(x, z, t))+(1/2)*gamma[1]*(-2*sin(theta(x, z, t))^2-cos(2*theta(x, z, t))))-(1/2)*gamma[1]*(4*sin(theta(x, z, t))^2*(diff(theta(x, z, t), t))+2*(diff(theta(x, z, t), t))*cos(2*theta(x, z, t)))+((diff(u(x, z, t), x))*gamma[2]-(diff(v(x, z, t), z))*gamma[2])*cos(theta(x, z, t))*sin(theta(x, z, t))+f[2](theta(x, z, t))*(diff(theta(x, z, t), x, x))+f[1](theta(x, z, t))*(diff(theta(x, z, t), z, z));

varchange := {t = T*tau, u = xi*h^2*U/alpha[4], v = xi*h^2*V/alpha[4], x = X*h, z = Z*h, K[3] = K[1]*k[3], f[1] = K[1]*F[1], f[2] = K[1]*F[2], gamma[1] = mu*Gamma[1], gamma[2] = mu*Gamma[2]};

PDEtools:-dchange(varchange, eqn, [tau, U, V, X, Z, k[3], F[1], F[2], GAMMA[1], GAMMA[2]]);

i want to label x,y axis with command...if i use manually ..i always need to do again after running..so how can i label x,y axis in this plot...? i watch manual and i din't find for axis..stress-strain.mwstress-strain.mw

in this equations...how to plot (a,e)? thank you guys

plot.mw

Can you change f(eta) to upflow curve and theta(eta) to downflow curve.

In my Problem,Boundary Conditions are

theta(infinity) = 0, (D(f))(infinity) = 1 , (Take, eta =infinity)

Flows will be correct for what value is taken for infinity .

I take  eta = 5. and also tried changing ranges  but could't find it.Please Help to fix the curve.

my code is,

SM.mw

How to solve ordinary differemtial equation system with initial conditions and boundary conditions. Here, some initial conditions are unknown variables. So how to find these  values of parameters.

eq1 := diff(f(x), x, x, x)+(1/2)*cos(alpha)*x*(diff(f(x), x, x))+(1/2)*sin(alpha)*f(x)*(diff(f(x), x, x)) = 0;

eq2 := diff(g(x), x, x)+diff(g(x), x)+(diff(g(x), x))*(diff(h(x), x))+cos(alpha)*x*(diff(g(x), x))+sin(alpha)*f(x)*g(x) = 0;

eq3 := diff(g(x), x, x)+diff(h(x), x, x)+1/2*(cos(alpha)*x+sin(alpha)*f(x)) = 0

ics:=f(0)=0, f'(0)=1, f''(0)=a[1], g(0)=1, g'(0)=a[2], h(0)=1, h'(0)=a[3];

bcs:=f(x) , g(x), h(x) tends to 0 ad x tends to infinity

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