Gabriel samaila

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4 years, 43 days

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These are questions asked by Gabriel samaila

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

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

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

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

 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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