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Gabriel samaila

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How to solve PDE in Maple...

Gabriel samaila 35 Maple 16 , MaplePrimes
pde
November 27 2021
0 0

Good day everyone, please I'm soliciting help on how to solve PDE in Maple. I know how to solve ODE but I don't know how to go about PDE. The problem I want to solve is attached as an attachment. If epsilon is zero, then the problem reduces to ODE which can easily be solved, but epsilon is not supposed to be zero. please I need your help, thank you in anticipation.

PDE.pdf

How to plot with numeric solution from d...

Gabriel samaila 35 Maple 16
ode homework numeric
May 15 2021
1 6

ishak.mw
 

> 

restart
> 

with*plots; -1; ode1 := diff(f(eta), eta, eta, eta)+(1/2)*f(eta)*(diff(f(eta), eta, eta)) = 0

diff(diff(diff(f(eta), eta), eta), eta)+(1/2)*f(eta)*(diff(diff(f(eta), eta), eta)) = 0

 (1)
> 

ode2 := (diff(theta(eta), eta, eta))/pr+3*N*f(eta)*(diff(theta(eta), eta))/(6*N+8) = 0

(diff(diff(theta(eta), eta), eta))/pr+3*N*f(eta)*(diff(theta(eta), eta))/(6*N+8) = 0

 (2)
> 

bcs1 := f(0) = 0, (D(f))(0) = S, (D(f))(16) = 1-S;

f(0) = 0, (D(f))(0) = S, (D(f))(16) = 1-S

 (3)
> 

fixedparameter := [pr = 1];

[pr = 1]

 (4)
> 

ode3 := eval(ode2, fixedparameter);

diff(diff(theta(eta), eta), eta)+3*N*f(eta)*(diff(theta(eta), eta))/(6*N+8) = 0

 (5)
> 

ode4 := eval(ode1, fixedparameter);

diff(diff(diff(f(eta), eta), eta), eta)+(1/2)*f(eta)*(diff(diff(f(eta), eta), eta)) = 0

 (6)
> 

bcs2 := theta(16) = 0, (D(theta))(0) = -a*(1-theta(0));

theta(16) = 0, (D(theta))(0) = -a*(1-theta(0))

 (7)

 

> 

L := [1, 5, 10]

[1, 5, 10]

 (8)
> 

 
  
> 

``
> 


  for k to 10 do
      sol_All := dsolve
                 ( eval
                   ( {bcs1, bcs2, ode3, ode4},
                     [N= L[k],a=1,S=1]
                   ),
                   [f(eta), theta(eta)],
                   numeric,
                   output = listprocedure
                 );
      Y_sol || k := rhs(sol_All[5]);
      YP_sol || k := -rhs(sol_All[6]);
feta || k := rhs(sol_All[4]);
      fpeta || k := rhs(sol_All[3])
  end do:

Error, invalid subscript selector

  
> 

for k to 10 do L[k], [(Y_sol || k)(0), (YP_sol || k)(0)] end do

1, [HFloat(0.8022978364702027), HFloat(0.19770216352979716)]

  

5, [HFloat(0.7250508085648081), HFloat(0.27494919143519203)]

  

10, [HFloat(0.7099202264181006), HFloat(0.29007977358189907)]

  

Error, invalid subscript selector

  
> 

for k to 10 do L[k], [(feta || k)(0)] end do

1, [HFloat(-0.4437495989448031)]

  

5, [HFloat(-0.4437495983315978)]

  

10, [HFloat(-0.4437495982077529)]

  

Error, invalid subscript selector

  
> 

``
> 

  plot( [ seq((Y_sol||j)(eta), j = 1..16)],
         eta = 0 .. 10,
         labels = [eta, theta(eta)],
         axes = boxed
      );
plot( [ seq((YP_sol||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, thetaprime(eta)],
         axes = boxed
      );

 plot( [ seq((feta||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, f(eta)],
         axes = boxed
      );
  plot( [ seq((fpeta||j)(eta), j = 1..6)],
         eta = 0 .. 8,
         labels = [eta, fprime(eta)],
         axes = boxed
      );

Warning, expecting only range variable eta in expression Y_sol4(eta) to be plotted but found name Y_sol4

  

 

Warning, expecting only range variable eta in expression YP_sol4(eta) to be plotted but found name YP_sol4

  

 

Warning, expecting only range variable eta in expression feta4(eta) to be plotted but found name feta4

  

 

Warning, expecting only range variable eta in expression fpeta4(eta) to be plotted but found name fpeta4

  

 
> 

NULL
> 

``
> 

NULL


 

Download ishak.mw

Good day every one;

please im soliciting for a help on how to plot my Nusselt number and Skin friction.

The attached is plotting against the dependent variable (eta) but i want skin friction (f  ' ' ) against N or Pr not against eta 

thank you for your help in aticipation

Exporting maple plot into MATLAB...

Gabriel samaila 35 Maple 16
matlab export plotting
September 03 2020
1 4

Hi every one

I'm having some plots in maple, but the layout is not pretty enough, I want export in to MATLAB. Does some one please have an idea on how I can go about it?.

I'm using Maple 16

Thank you in anticipation

Adomian Decomposition...

Gabriel samaila 35 Maple
homework differential-equations adomian-decomposition
September 21 2019
0 0

Hi guys,

I'm trying to apply boundary condition on the seris i generated using Adomian decomposition. Could some one please check it for me?
 

NULL

> 

u[0] := a1+a2*y:
> 

NULL
> 

NULL
> 

w[0] := a3+a4*y:
> 

theta[0] := a6*y+a5
> 

phi[0] := a8*y+a7
> 

NULL
> 

NULL
> 

``
> 

``
> 

``
> 

``
> 

``
> 

A[1] := R*(diff(u[0], y))+A-Gr*(B*phi[0]+theta[0])/Ree+Ha^2*(alpha*u[0]+beta*w[0])/(alpha^2+beta^2)

R*a2+A-Gr*(a5+a6*y+B*(a7+a8*y))/Ree+Ha^2*(alpha*(a1+a2*y)+beta*(a3+a4*y))/(alpha^2+beta^2)

 (1)
> 

u[1] := int(A[1], y = 0 .. y)

(1/2)*(-Gr*(a6+B*a8)/Ree+Ha^2*(alpha*a2+beta*a4)/(alpha^2+beta^2))*y^2+R*a2*y+A*y-Gr*(a5+B*a7)*y/Ree+Ha^2*(alpha*a1+beta*a3)*y/(alpha^2+beta^2)

 (2)
> 

u[11] := int(u[1], y = 0 .. y)

(1/3)*(-(1/2)*Gr*(a6+B*a8)/Ree+(1/2)*Ha^2*(alpha*a2+beta*a4)/(alpha^2+beta^2))*y^3+(1/2)*(R*a2+A-Gr*(a5+B*a7)/Ree+Ha^2*(alpha*a1+beta*a3)/(alpha^2+beta^2))*y^2

 (3)
> 

u = u[0]+u[11]

u = a1+a2*y+(1/3)*(-(1/2)*Gr*(a6+B*a8)/Ree+(1/2)*Ha^2*(alpha*a2+beta*a4)/(alpha^2+beta^2))*y^3+(1/2)*(R*a2+A-Gr*(a5+B*a7)/Ree+Ha^2*(alpha*a1+beta*a3)/(alpha^2+beta^2))*y^2

 (4)
> 

> 

A[2] := R*(diff(w[0], y))-Ha^2*(beta*u[0]-alpha*w[0])/(alpha^2+beta^2)

R*a4-Ha^2*(beta*(a1+a2*y)-alpha*(a3+a4*y))/(alpha^2+beta^2)

 (5)
> 

w[1] := int(A[2], y = 0 .. y)

-(1/2)*Ha^2*(beta*a2-alpha*a4)*y^2/(alpha^2+beta^2)+R*a4*y-Ha^2*(beta*a1-alpha*a3)*y/(alpha^2+beta^2)

 (6)
> 

w[11] := int(w[1], y = 0 .. y)

-(1/6)*Ha^2*(beta*a2-alpha*a4)*y^3/(alpha^2+beta^2)+(1/2)*(R*a4-Ha^2*(beta*a1-alpha*a3)/(alpha^2+beta^2))*y^2

 (7)
> 

``
> 

w = w[0]+w[11]

w = a3+a4*y-(1/6)*Ha^2*(beta*a2-alpha*a4)*y^3/(alpha^2+beta^2)+(1/2)*(R*a4-Ha^2*(beta*a1-alpha*a3)/(alpha^2+beta^2))*y^2

 (8)
> 

A[3] := R*Pr*(diff(theta[0], y))-2*Br*((diff(u[0], y))^2+(diff(w[0], y))^2+M^2*C*(u[0]^2+w[0]^2))-gamma*R*Pr*theta[0]

R*Pr*a6-2*Br*(a2^2+a4^2+M^2*C*((a1+a2*y)^2+(a3+a4*y)^2))-gamma*R*Pr*(a5+a6*y)

 (9)
> 

theta[1] := int(A[3], y = 0 .. y)

-(2/3)*Br*M^2*C*(a2^2+a4^2)*y^3+(1/2)*(-2*Br*M^2*C*(2*a1*a2+2*a3*a4)-gamma*R*Pr*a6)*y^2+R*Pr*a6*y-2*Br*(a2^2+a4^2+M^2*C*(a1^2+a3^2))*y-gamma*R*Pr*a5*y

 (10)
> 

theta[11] := int(theta[1], y = 0 .. y)

-(1/6)*Br*M^2*C*(a2^2+a4^2)*y^4+(1/3)*(-Br*M^2*C*(2*a1*a2+2*a3*a4)-(1/2)*gamma*R*Pr*a6)*y^3+(1/2)*(R*Pr*a6-2*Br*(a2^2+a4^2+M^2*C*(a1^2+a3^2))-gamma*R*Pr*a5)*y^2

 (11)
> 

theta = theta[0]+theta[11]

theta = a5+a6*y-(1/6)*Br*M^2*C*(a2^2+a4^2)*y^4+(1/3)*(-Br*M^2*C*(2*a1*a2+2*a3*a4)-(1/2)*gamma*R*Pr*a6)*y^3+(1/2)*(R*Pr*a6-2*Br*(a2^2+a4^2+M^2*C*(a1^2+a3^2))-gamma*R*Pr*a5)*y^2

 (12)
> 

``

 

NULL

> 

A[4] := R*Sc*(diff(phi[0], y))-K*Sc*phi[0]

R*Sc*a8-K*Sc*(a7+a8*y)

 (13)
> 

phi[1] := int(A[4], y = 0 .. y)

-(1/2)*K*Sc*a8*y^2+R*Sc*a8*y-K*Sc*a7*y

 (14)
> 

phi[11] := int(phi[1], y = 0 .. y)

-(1/6)*K*Sc*a8*y^3+(1/2)*(R*Sc*a8-K*Sc*a7)*y^2

 (15)
> 

phi = phi[0]+phi[11]

phi = a7+a8*y-(1/6)*K*Sc*a8*y^3+(1/2)*(R*Sc*a8-K*Sc*a7)*y^2

 (16)
> 

``


 

Download second_problem.mw

homotopy pertubation...

Gabriel samaila 35 Maple 2016
numeric differential-equations
May 23 2019
1 3

 Hi guys,
I am trying write a code for homotopy perturbation, i have already generated the polynomial as you can see, i have also  solve for concentration equation since is not couple. But i have a lot of error massages for temperature, velocity and induced magnetic field. can some one please go through the code?
 

NULL

> 

restart
> 

PDEtools[declare](f(x),theta(x),u(x),w(x), prime=x):

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

  

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

  

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

  

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

  

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

 (1)
> 

N := 4:
> 

NULL

NULL

> 

f(x):=sum((p^(i))*f[i](x),i=0..N);

f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x)+p^4*f[4](x)

 (2)
> 

theta(x) := sum(p^i*theta[i](x), i = 0 .. N);

theta[0](x)+p*theta[1](x)+p^2*theta[2](x)+p^3*theta[3](x)+p^4*theta[4](x)

 (3)
> 

``
> 

u(x) := sum(p^i*u[i](x), i = 0 .. N);

u[0](x)+p*u[1](x)+p^2*u[2](x)+p^3*u[3](x)+p^4*u[4](x)

 (4)
> 

``
> 

w(x) := sum(p^i*w[i](x), i = 0 .. N);

w[0](x)+p*w[1](x)+p^2*w[2](x)+p^3*w[3](x)+p^4*w[4](x)

 (5)
> 

HPMEq := (1-p)*(diff(f(x), `$`(x, 2)))+p*(diff(f(x), `$`(x, 2))-k1*(diff(f(x), x))-k2*f(x));

(1-p)*(diff(diff(f[0](x), x), x)+p*(diff(diff(f[1](x), x), x))+p^2*(diff(diff(f[2](x), x), x))+p^3*(diff(diff(f[3](x), x), x))+p^4*(diff(diff(f[4](x), x), x)))+p*(diff(diff(f[0](x), x), x)+p*(diff(diff(f[1](x), x), x))+p^2*(diff(diff(f[2](x), x), x))+p^3*(diff(diff(f[3](x), x), x))+p^4*(diff(diff(f[4](x), x), x))-k1*(diff(f[0](x), x)+p*(diff(f[1](x), x))+p^2*(diff(f[2](x), x))+p^3*(diff(f[3](x), x))+p^4*(diff(f[4](x), x)))-k2*(f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x)+p^4*f[4](x)))

 (6)
> 

HPMEr := (1-p)*(diff(theta(x), `$`(x, 2)))+p*(diff(theta(x), `$`(x, 2))-k11*(diff(theta(x), x))+k12*(diff(u(x), x))^2+k13*(diff(w(x), x))^2+k14*theta(x));

(1-p)*(diff(diff(theta[0](x), x), x)+p*(diff(diff(theta[1](x), x), x))+p^2*(diff(diff(theta[2](x), x), x))+p^3*(diff(diff(theta[3](x), x), x))+p^4*(diff(diff(theta[4](x), x), x)))+p*(diff(diff(theta[0](x), x), x)+p*(diff(diff(theta[1](x), x), x))+p^2*(diff(diff(theta[2](x), x), x))+p^3*(diff(diff(theta[3](x), x), x))+p^4*(diff(diff(theta[4](x), x), x))-k11*(diff(theta[0](x), x)+p*(diff(theta[1](x), x))+p^2*(diff(theta[2](x), x))+p^3*(diff(theta[3](x), x))+p^4*(diff(theta[4](x), x)))+k12*(diff(u[0](x), x)+p*(diff(u[1](x), x))+p^2*(diff(u[2](x), x))+p^3*(diff(u[3](x), x))+p^4*(diff(u[4](x), x)))^2+k13*(diff(w[0](x), x)+p*(diff(w[1](x), x))+p^2*(diff(w[2](x), x))+p^3*(diff(w[3](x), x))+p^4*(diff(w[4](x), x)))^2+k14*(theta[0](x)+p*theta[1](x)+p^2*theta[2](x)+p^3*theta[3](x)+p^4*theta[4](x)))

 (7)
> 

HPMEs := (1-p)*(diff(u(x), `$`(x, 2)))+p*(diff(u(x), `$`(x, 2))-R*(diff(u(x), x))-A-k8*w(x)-k7*u(x)+k5*theta(x)+k6*f(x));

(1-p)*(diff(diff(u[0](x), x), x)+p*(diff(diff(u[1](x), x), x))+p^2*(diff(diff(u[2](x), x), x))+p^3*(diff(diff(u[3](x), x), x))+p^4*(diff(diff(u[4](x), x), x)))+p*(diff(diff(u[0](x), x), x)+p*(diff(diff(u[1](x), x), x))+p^2*(diff(diff(u[2](x), x), x))+p^3*(diff(diff(u[3](x), x), x))+p^4*(diff(diff(u[4](x), x), x))-R*(diff(u[0](x), x)+p*(diff(u[1](x), x))+p^2*(diff(u[2](x), x))+p^3*(diff(u[3](x), x))+p^4*(diff(u[4](x), x)))-A-k8*(w[0](x)+p*w[1](x)+p^2*w[2](x)+p^3*w[3](x)+p^4*w[4](x))-k7*(u[0](x)+p*u[1](x)+p^2*u[2](x)+p^3*u[3](x)+p^4*u[4](x))+k5*(theta[0](x)+p*theta[1](x)+p^2*theta[2](x)+p^3*theta[3](x)+p^4*theta[4](x))+k6*(f[0](x)+p*f[1](x)+p^2*f[2](x)+p^3*f[3](x)+p^4*f[4](x)))

 (8)
> 

HPMEt := (1-p)*(diff(w(x), `$`(x, 2)))+p*(diff(w(x), `$`(x, 2))-R*(diff(w(x), x))+k9*u(x)-k10*w(x))

(1-p)*(diff(diff(w[0](x), x), x)+p*(diff(diff(w[1](x), x), x))+p^2*(diff(diff(w[2](x), x), x))+p^3*(diff(diff(w[3](x), x), x))+p^4*(diff(diff(w[4](x), x), x)))+p*(diff(diff(w[0](x), x), x)+p*(diff(diff(w[1](x), x), x))+p^2*(diff(diff(w[2](x), x), x))+p^3*(diff(diff(w[3](x), x), x))+p^4*(diff(diff(w[4](x), x), x))-R*(diff(w[0](x), x)+p*(diff(w[1](x), x))+p^2*(diff(w[2](x), x))+p^3*(diff(w[3](x), x))+p^4*(diff(w[4](x), x)))+k9*(u[0](x)+p*u[1](x)+p^2*u[2](x)+p^3*u[3](x)+p^4*u[4](x))-k10*(w[0](x)+p*w[1](x)+p^2*w[2](x)+p^3*w[3](x)+p^4*w[4](x)))

 (9)
> 

for i from 0 to N do equ[1][i] := coeff(HPMEq, p, i) = 0 end do;

diff(diff(f[0](x), x), x) = 0

  

diff(diff(f[1](x), x), x)-k1*(diff(f[0](x), x))-k2*f[0](x) = 0

  

diff(diff(f[2](x), x), x)-k2*f[1](x)-k1*(diff(f[1](x), x)) = 0

  

diff(diff(f[3](x), x), x)-k2*f[2](x)-k1*(diff(f[2](x), x)) = 0

  

diff(diff(f[4](x), x), x)-k1*(diff(f[3](x), x))-k2*f[3](x) = 0

 (10)
> 

for i from 0 to N do equa[1][i] := coeff(HPMEr, p, i) = 0 end do;

diff(diff(theta[0](x), x), x) = 0

  

diff(diff(theta[1](x), x), x)-k11*(diff(theta[0](x), x))+k12*(diff(u[0](x), x))^2+k13*(diff(w[0](x), x))^2+k14*theta[0](x) = 0

  

diff(diff(theta[2](x), x), x)+2*k13*(diff(w[0](x), x))*(diff(w[1](x), x))-k11*(diff(theta[1](x), x))+2*k12*(diff(u[0](x), x))*(diff(u[1](x), x))+k14*theta[1](x) = 0

  

diff(diff(theta[3](x), x), x)+k12*(2*(diff(u[0](x), x))*(diff(u[2](x), x))+(diff(u[1](x), x))^2)+k14*theta[2](x)+k13*(2*(diff(w[0](x), x))*(diff(w[2](x), x))+(diff(w[1](x), x))^2)-k11*(diff(theta[2](x), x)) = 0

  

diff(diff(theta[4](x), x), x)+k12*(2*(diff(u[0](x), x))*(diff(u[3](x), x))+2*(diff(u[1](x), x))*(diff(u[2](x), x)))-k11*(diff(theta[3](x), x))+k14*theta[3](x)+k13*(2*(diff(w[0](x), x))*(diff(w[3](x), x))+2*(diff(w[1](x), x))*(diff(w[2](x), x))) = 0

 (11)
> 

for i from 0 to N do equat[1][i] := coeff(HPMEs, p, i) = 0 end do;

diff(diff(u[0](x), x), x) = 0

  

diff(diff(u[1](x), x), x)-R*(diff(u[0](x), x))-A-k7*u[0](x)+k5*theta[0](x)+k6*f[0](x)-k8*w[0](x) = 0

  

diff(diff(u[2](x), x), x)-R*(diff(u[1](x), x))-k7*u[1](x)+k6*f[1](x)-k8*w[1](x)+k5*theta[1](x) = 0

  

diff(diff(u[3](x), x), x)-R*(diff(u[2](x), x))+k6*f[2](x)-k7*u[2](x)+k5*theta[2](x)-k8*w[2](x) = 0

  

diff(diff(u[4](x), x), x)-R*(diff(u[3](x), x))+k5*theta[3](x)+k6*f[3](x)-k7*u[3](x)-k8*w[3](x) = 0

 (12)
> 

``
> 

for i from 0 to N do equati[1][i] := coeff(HPMEt, p, i) = 0 end do;

diff(diff(w[0](x), x), x) = 0

  

diff(diff(w[1](x), x), x)-R*(diff(w[0](x), x))-k10*w[0](x)+k9*u[0](x) = 0

  

diff(diff(w[2](x), x), x)-k10*w[1](x)+k9*u[1](x)-R*(diff(w[1](x), x)) = 0

  

diff(diff(w[3](x), x), x)-k10*w[2](x)+k9*u[2](x)-R*(diff(w[2](x), x)) = 0

  

diff(diff(w[4](x), x), x)+k9*u[3](x)-R*(diff(w[3](x), x))-k10*w[3](x) = 0

 (13)
> 

con[1][0] := f[0](-1) = 1, f[0](1) = 1:

-.5000000000*k2+0.3435019841e-1*k2^4+.5000000000*k2*x^2-.2500000000*k2^2*x^2+.2083333333*k2^2+0.4166666667e-1*k2^2*x^4-0.2083333333e-1*k2^3*x^4+.1041666667*k2^3*x^2+0.4166666667e-1*k1^2*k2+0.5952380952e-3*k2^3*k1*x^7-0.8472222222e-1*k2^3+0.2480158730e-4*k2^4*x^8+0.4166666667e-2*x^6*k1^2*k2^2+0.8333333333e-2*k2*x^5*k1^3-0.9722222222e-2*k1*k2^3*x^5-0.3472222222e-1*k1^2*k2^2*x^4-0.2777777778e-1*k2*x^3*k1^3+0.5046296296e-1*k1*k2^3*x^3+0.6805555556e-1*k2^2*k1^2*x^2-0.4133597884e-1*k1*k2^3*x+0.1944444444e-1*k2*k1^3*x+1.+0.1388888889e-2*k2^3*x^6+0.1666666667e-1*k1*k2^2*x^5+0.4166666667e-1*k2*x^4*k1^2-.1111111111*k2^2*k1*x^3+0.9444444444e-1*k1*k2^2*x-0.8333333333e-1*k2*k1^2*x^2+.1666666667*k2*k1*x^3-0.3750000000e-1*k1^2*k2^2-0.6944444444e-3*k2^4*x^6+0.8680555556e-2*k2^4*x^4-0.4236111111e-1*k2^4*x^2-.1666666667*k1*k2*x

  

1-(1/2)*k2+(277/8064)*k2^4+(1/2)*k2*x^2-(1/4)*k2^2*x^2+(5/24)*k2^2+(1/24)*k2^2*x^4-(1/48)*k2^3*x^4+(5/48)*k2^3*x^2+(1/24)*k1^2*k2+(1/1680)*k2^3*k1*x^7-(61/720)*k2^3+(1/40320)*k2^4*x^8+(1/240)*x^6*k1^2*k2^2+(1/120)*k2*x^5*k1^3-(7/720)*k1*k2^3*x^5-(5/144)*k1^2*k2^2*x^4-(1/36)*k2*x^3*k1^3+(109/2160)*k1*k2^3*x^3+(49/720)*k2^2*k1^2*x^2-(125/3024)*k1*k2^3*x+(7/360)*k2*k1^3*x+(1/720)*k2^3*x^6+(1/60)*k1*k2^2*x^5+(1/24)*k2*x^4*k1^2-(1/9)*k2^2*k1*x^3+(17/180)*k1*k2^2*x-(1/12)*k2*k1^2*x^2+(1/6)*k2*k1*x^3-(3/80)*k1^2*k2^2-(1/1440)*k2^4*x^6+(5/576)*k2^4*x^4-(61/1440)*k2^4*x^2-(1/6)*k1*k2*x

  

2.400000000*k2+0.3589208394e-1*k2^4+1.104000000*k2^2+2.713333334*k1*k2+1.904000000*k1^2*k2+0.115520003e-1*k2^3+.939244445*k1*k2^2+.3973226666*k1^2*k2^2+0.1412642116e-1*k1*k2^3+.9218444444*k1^3*k2

 (14)

NULL

> 

"cond[1][0]:=theta[0](-1)=0.1, theta[0](1)=1,w[0](-1)=0, w[0](1)=0,u[0](-1)=0, u[0](1)=0: for j from 1 to N do: cond[1][j]:=theta[j](-1)=0, theta[j](1)=0,w[j](-1)=0, w[j](1)=0,u[j](-1)=0, u[j](1)=0: end do: for i from 0 to N do: dsolve({equa[1][i],cond[1][i]},theta[i](x)); theta[i](x):=rhs(`%`): end do: theta(x):=evalf(simplify(sum(theta[n](x),n=0..N))); convert(theta(x),'rational'); "

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {u[0](-1) = 0, u[0](1) = 0, w[0](-1) = 0, w[0](1) = 0}

  

theta[0](x)+theta[1](x)+theta[2](x)+theta[3](x)+theta[4](x)

  

theta[0](x)+theta[1](x)+theta[2](x)+theta[3](x)+theta[4](x)

 (15)
> 

``
> 

"condi[1][0]:=theta[0](-1)=0.1, theta[0](1)=1,w[0](-1)=0, w[0](1)=0,u[0](-1)=0, u[0](1)=0,f[0](-1)=1, f[0](1)=1: for j from 1 to N do: condi[1][j]:=theta[j](-1)=0, theta[j](1)=0,w[j](-1)=0, w[j](1)=0,u[j](-1)=0, u[j](1)=0, f[j](-1)=0, f[j](1)=0: end do: for i from 0 to N do: dsolve({equat[1][i],condi[1][i]},u[i](x)); u[i](x):=rhs(`%`): end do: u(x):=evalf(simplify(sum(u[n](x),n=0..N)))"

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {f[0](-1) = 1, f[0](1) = 1, w[0](-1) = 0, w[0](1) = 0, theta[0](-1) = 1/10, theta[0](1) = 1}

  

u[0](x)+u[1](x)+u[2](x)+u[3](x)+u[4](x)

 (16)

``

> 

"condit[1][0]:=theta[0](-1)=0.1, theta[0](1)=1,w[0](-1)=0, w[0](1)=0,u[0](-1)=0, u[0](1)=0,f[0](-1)=1, f[0](1)=1: for j from 1 to N do: condit[1][j]:=theta[j](-1)=0, theta[j](1)=0,w[j](-1)=0, w[j](1)=0,u[j](-1)=0, u[j](1)=0, f[j](-1)=0, f[j](1)=0: end do: for i from 0 to N do: dsolve({equati[1][i],condit[1][i]},w[i](x)); w[i](x):=rhs(`%`): end do: w(x):=evalf(simplify(sum(w[n](x),n=0..N)))"

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {f[0](-1) = 1, f[0](1) = 1, u[0](-1) = 0, u[0](1) = 0, theta[0](-1) = 1/10, theta[0](1) = 1}

  

w[0](x)+w[1](x)+w[2](x)+w[3](x)+w[4](x)

 (17)

NULL

> 

``
> 

``


 

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