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How to get theta(2),theta(3),...?...

Saha 70 Maple 18
syntax homework user-error
December 22 2022
2 3

Thermal_Stress_Distribution.mw

Could you please help me to rectify this error.
> 

restart
> 

with(PDEtools):
> 

"Theta[0]:=1:Theta[1]:=Gamma:delta(0):=1:for w from 1 to 30 do delta(w):=0;od:delta(-1):=0:beta:=2:N[cc]:=1:N[rc]:=0.5:Q[int]:=0.2:gamma:=0.3:Mu:=0.5:Theta[a]:=0.2: "

Error, attempting to assign to `gamma` which is protected.  Try declaring `local gamma`; see ?protect for details.

  
> 

> 

for k from 0 to 8 do Theta(v+2) := solve(sum(delta[w-1]*(v-w+1)*(v-w+2)*Theta[v-w+2], w = 0 .. v)-Q[int]*gamma*Theta[a]*delta[v]-Q[int]*gamma*delta[v-1]*Theta[a]+M*Theta[a]*delta[v]/(1-Theta[a])+M*Theta[a]*delta[v-1]/(1-Theta[a])-M*(sum(delta[w-1]*Theta[v-w], w = 0 .. v))/(1-Theta[a])-M*Theta[v]/(1-Theta[a])+N[rc]*Theta[a]^4*delta[v-1]+Q[int]*gamma*(sum(delta[w-1]*Theta[v-w], w = 0 .. v))+Q[int]*gamma*delta[v]+N[cc]*Theta[a]*delta[v-1]+N[rc]*Theta[a]^4*delta[v]+N[cc]*Theta[a]*delta[v]+(v+1)*(v+2)*Theta[v+2]+Q[int]*delta[v-1]+Q[int]*delta[v]-N[rc]*(sum(sum(sum(sum(delta[l-1]*Theta[w-l]*Theta[Zeta-w]*Theta[w-Zeta]*Theta[v-w], l = 0 .. w), w = 0 .. Zeta), Zeta = 0 .. w), w = 0 .. v))-N[rc]*(sum(sum(sum(Theta[w]*Theta[Zeta-w]*Theta[w-Zeta]*Theta[v-w], w = 0 .. Zeta), Zeta = 0 .. w), w = 0 .. v))-N[cc]*(sum(delta[w-1]*Theta[v-w], w = 0 .. v))+beta*(sum(sum(delta[Zeta-1]*(w-Zeta+1)*Theta[w-Zeta+1]*(v-w+1)*Theta[v-w+1], Zeta = 0 .. w), w = 0 .. v))-N[cc]*Theta[v]+beta*(sum(Theta[v-w]*(w+1)*Theta[w+1], w = 0 .. v))+(v+1)*Theta[v+1]+beta*(sum((v-w+1)*Theta[v-w+1]*(w+1)*Theta[w+1], w = 0 .. v))+beta*(sum(Theta[v-w]*(w+1)(w+2)*Theta[w+2], w = 0 .. v))+beta*(sum(sum(delta[Zeta-1]*Theta[w-m]*(v-w+1)*(v-w+2)*Theta[v-w+2], Zeta = 0 .. w), w = 0 .. v)), Theta(v+2)) end do

Error, invalid left hand side in assignment

  
> 

``

Download Thermal_Stress_Distribution.mw

"How do I solve this''?...

Saha 70 Maple 18
syntax user-error
December 18 2022
2 0

PROBLEM-IP.mw

What to do to get an upward curve in f(eta) and downward curve in theta(eta)?I get the curve wrong.Please Help.
> 

restart``
> 

with(PDEtools):
> 

ODE1 := diff(f(x), x, x, x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[f(x)])*(eta*cos(omega)+f(x)*`sinω`)*(diff(f(x), x, x))+(1-phi)^2.5*M*sin(alpha)^2*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[f(x)])*Gr[x]*`cosγ`*theta = 0;

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[f(x)])*(eta*cos(omega)+f(x)*`sinω`)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin(alpha)^2*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[f(x)])*Gr[x]*`cosγ`*theta = 0

 (1)
> 

ODE2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(eta*cos(omega)+`sinω`*f)*(diff(theta(x), x)) = 0;

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(eta*cos(omega)+`sinω`*f)*(diff(theta(x), x)) = 0

 (2)
> 

Implementation*of*Differential*Transformation*Method*(Fe[3]*O[4]-Water);

Implementation*of*Differential*DifferentialGeometry:-Transformation*Method*(Fe[3]*O[4]-Water)

 (3)
> 

rho[s] := 5200:
> 

for k from 0 to 15 do F(k+3) := -((1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[f])*(sum((m+1)*(m+2)*F(m+2)*(cos(omega)*delta(k-m+1)+sin(omega)*F(k-m)), m = 0 .. k))+(1-phi)^2.5*M*sin(alpha)^2*(1-(k+1)*F(k+1))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[f])*Gr[x]*cos*gamma*Theta(k))/((k+1)*(k+2)*(k+3)) end do:
> 

for k from 0 to 15 do Theta(k+2) := -(1/2)*Pr*(sum((m+1)*Theta(m+1)*(cos(omega)*delta(k-m+1)+sin(omega)*F(k-m)), m = 0 .. k))/((k+1)*(k+2)*K[nf]) end do:
> 

f(eta) := simplify(sum(F(i)*eta^i, i = 0 .. 5), symbolic):
> 

indets(f(eta));

{A, B, M, alpha, cos, eta, omega, phi, Gr[x], (1.-phi)^(1/2), sin(alpha), sin(omega)}

 (4)
> 

Theta(eta) := simplify(sum(Theta(i)*eta^i, i = 0 .. 5), symbolic):
> 

indets(Theta(eta));

{A, B, M, Pr, alpha, cos, eta, omega, phi, Gr[x], (1.-phi)^(1/2), sin(alpha), sin(omega)}

 (5)
> 

> 

U := subs(M = 1, phi = .1, sin(alpha) = 1, cos(omega) = 1, sin(omega) = 0, cos*gamma = 1/sqrt(2), Gr[x] = 0, Pr = 6.2, `ρβ`[f] = 20939.1, K[nf] = .6842, f(eta));

(A-0.3201806132e-1*eta^2-0.1772797452e-1*eta^3-.1280722452*eta+0.6403612263e-1*eta^2*A)*eta^2

 (6)
> 

V := subs(Pr = 6.2, phi = .1, sin(alpha) = 1, M = 1, cos(omega) = 1, sin(omega) = 0, Gr[x] = 0, cos(gamma) = 1/sqrt(2), `ρβ`[f] = 20939.1, K[nf] = .6842, Theta(eta));

1.000000000+1.000000000*B*eta

 (7)
> 

e1 := subs(eta = 0, U) = 0;

0 = 0

  

diff*(0, 0) = 0

  

-14.09573093+12.91590125*A = 1

  

1.000000000 = 1

  

1.000000000+3.000000000*B = 0

  

{1.000000000 = 1, -14.09573093+12.91590125*A = 1, 1.000000000+3.000000000*B = 0}

  

{A = 1.168771009, B = -.3333333333}

 (8)
> 

U1 := subs(A = 1.168771009, B = -.3333333333, U);

(1.168771009+0.4282550234e-1*eta^2-0.1772797452e-1*eta^3-.1280722452*eta)*eta^2

 (9)
> 

V1 := subs(A = 1.168771009, B = -.3333333333, V);

1.000000000-.3333333333*eta

 (10)
> 

p1 := M = 1, phi = .1, A = 1.168771009*(1/2), B = -.3333333333, sin(alpha) = 1, cos(omega) = 1, sin(omega) = 0, cos*gamma = 1/sqrt(2), Gr[x] = 0, Pr = 6.2:
> 

s1 := subs(p1, f(eta)):
> 

d1 := diff(s1, `$`(eta, 1)):
> 

plot([d1, d2, d3], eta = 0 .. 1);

Warning, expecting only range variable eta in expression (.1080744102e-1*eta-.7183594026e-1*eta^2-.1280722452-.3441379740e-1*cos+.5735632896e-2*eta*cos-.3966707070e-2*eta^2*cos)*eta^2+2*(.5843855045+.540372051e-2*eta^2-.2394531342e-1*eta^3-.1280722452*eta-.3441379740e-1*eta*cos+.2867816448e-2*eta^2*cos-.1322235690e-2*eta^3*cos)*eta to be plotted but found name cos

  

 
> 

p1 := M = 1, phi = .1, A = 1.168771009*(1/2), B = -.3333333333, sin(alpha) = 1, cos(omega) = 1, sin(omega) = 0, cos*gamma = 1/sqrt(2), Gr[x] = 0, Pr = 6.2:
> 

s1 := subs(p1, Theta(eta)):
> 

plot([s1, s2, s3], eta = 0 .. 1);

Warning, expecting only range variable eta in expression 1.000000000-.3333333333*eta+.6611393405e-1*eta^4-.8693603699e-2*eta^5-.2336024612e-2*eta^5*cos to be plotted but found name cos

  

 
> 

``

Download PROBLEM-IP.mw

''How to plot a curve ?"...

Saha 70 Maple 18
homework plotting duplicate-question
December 12 2022
1 0

Please Help! I am a beginner in using maple, I am getting  error in theta(k+2).How to get  m1,m2,m3 values from theta(k+2) and how to plot a curve theta(eta) like,f(eta). pp_DTM.mw

Download pp_DTM.mw

''How to rectify this error?''...

Saha 70 Maple 18
plotting
December 09 2022
2 0

Please help! How to solve this?

pp-velocity.mw

How to plot this Equation in Runge-Kutta...

Saha 70 Maple
ode homework dsolve
September 02 2022
1 1
I am trying to solve this equation in RK Method 4th-5th Order but the following error keeps happening.Please help me to solve this equations.
> 

restart
> 

with(PDETools, declare):
> 

with(LinearAlgebra):
> 

with(PolynomialIdeals):
> 

with(plots):
> 

declare(f(x));

f(x)*`will now be displayed as`*f

 (1)
> 

ODE1 := (diff(f(x), x, x, x))/((1-phi)^2.5*(1-phi+phi*rho[s]/rho[f(x)]))+(1/2)(`cosα`)*eta*(diff(f(x), x, x))+(1/2)(`sinα`)*f(x)*(diff(f(x), x, x))-M(diff(f(x), x)-1)/(1-phi+phi*rho[s]/rho[f(x)]) = 0:

(diff(diff(diff(f(x), x), x), x))/((1-phi)^2.5*(1-phi+phi*rho[s]/rho[f(x)]))+(1/2)*cos(alpha)*eta*(diff(diff(f(x), x), x))+(1/2)*sin(alpha)*f(x)*(diff(diff(f(x), x), x))-M(diff(f(x), x)-1)/(1-phi+phi*rho[s]/rho[f(x)]) = 0

 (2)
> 

ODE2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(1-phi+phi*rho[s]*c[s]/(rho[f]*c[f]))(eta*`cosα`+f*`sinα`)*(diff(theta(x), x)) = 0:

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(1-phi+phi*rho[s]*c[s]/(rho[f]*c[f]))*(cos(alpha)*eta+sin(alpha)*f(x))*(diff(theta(x), x)) = 0

 (3)
> 

bcs := f(0) = 0, (D(f))(0) = 0, (D(f))(25) = 1;

f(0) = 0, (D(f))(0) = 0, (D(f))(25) = 1

  

theta(0) = 1

 (4)
> 

a1 := [phi = .1, rho[s] = 5200, rho[f] = 997.1, c[s] = 670, c[f] = 4179, M = 1, sin(alpha) = 0, cos(alpha) = 1];

[phi = .1, rho[s] = 5200, rho[f] = 997.1, c[s] = 670, c[f] = 4179, M = 1, sin(alpha) = 0, cos(alpha) = 1]

  

[phi = .1, rho[s] = 5200, rho[f] = 997.1, c[s] = 670, c[f] = 4179, M = 1, sin(alpha) = 1, cos(alpha) = 0]

  

[phi = .1, rho[s] = 5200, rho[f] = 997.1, c[s] = 670, c[f] = 4179, M = 1, sin(alpha) = (1/2)*3^(1/2), cos(alpha) = 1/2]

  

[phi = .1, rho[s] = 5200, rho[f] = 997.1, c[s] = 670, c[f] = 4179, M = 1, sin(alpha) = 0, cos(alpha) = 1]

  

[phi = .1, rho[s] = 5200, rho[f] = 997.1, c[s] = 670, c[f] = 4179, K[nf] = .6842, Pr = 6.2, M = 1, sin(alpha) = 1, cos(alpha) = 0, K[f] = .613]

  

[phi = .1, rho[s] = 5200, rho[f] = 997.1, c[s] = 670, c[f] = 4179, K[nf] = .6842, Pr = 6.2, M = 1, sin(alpha) = (1/2)*3^(1/2), cos(alpha) = 1/2, K[f] = .613]

 (5)
> 

b1 := subs(a1, ode1);

1.301348831*(diff(diff(diff(f(x), x), x), x))/(.9+520.0/rho[f(x)])+(1/2)*eta*(diff(diff(f(x), x), x))-(1)(diff(f(x), x)-1)/(.9+520.0/rho[f(x)]) = 0

  

1.301348831*(diff(diff(diff(f(x), x), x), x))/(.9+520.0/rho[f(x)])+(1/2)*f(x)*(diff(diff(f(x), x), x))-(1)(diff(f(x), x)-1)/(.9+520.0/rho[f(x)]) = 0

  

1.301348831*(diff(diff(diff(f(x), x), x), x))/(.9+520.0/rho[f(x)])+(1/4)*eta*(diff(diff(f(x), x), x))+(1/4)*3^(1/2)*f(x)*(diff(diff(f(x), x), x))-(1)(diff(f(x), x)-1)/(.9+520.0/rho[f(x)]) = 0

  

1.301348831*(diff(diff(diff(f(x), x), x), x))/(.9+520.0/rho[f(x)])+(1/2)*eta*(diff(diff(f(x), x), x))-(1)(diff(f(x), x)-1)/(.9+520.0/rho[f(x)]) = 0

  

1.116150082*(diff(diff(theta(x), x), x))+3.049196273*f(x)*(diff(theta(x), x)) = 0

  

1.116150082*(diff(diff(theta(x), x), x))+3.049196273*((1/2)*eta+(1/2)*3^(1/2)*f(x))*(diff(theta(x), x)) = 0

 (6)
> 

c1 := dsolve({b1, bcs}, numeric); c1(0); c2 := dsolve({b2, bcs}, numeric); c2(0); c3 := dsolve({b3, bcs}, numeric); c3(0); c4 := dsolve({b4, bcs}, numeric); c4(0); c5 := dsolve({b5, bcs1}, numeric); c5(0)

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 5, got 3

  

c1(0)

  

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 4, got 3

  

c2(0)

  

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 5, got 3

  

c3(0)

  

Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 5, got 3

  

c4(0)

  

Error, (in dsolve/numeric/DAE/make_proc) number of unknown functions and equations must match, got 2 functions {f, theta}, and 1 equations

  

c5(0)

 (7)
> 

NULL

Download HP-Numeric.mw

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