Newton iteration not converging

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Question:Newton iteration not converging

Posted: gabbbooooo 5 Product: Maple 2022

September 05 2023

Good day all,

please I am new Maple user, i used the same code to solve boundary layer flow. Itried to use the same code in solving nanofluid but the solution is not coverging at some point. But the author i want to compared my results with had solution at those points.

Is there any way i can get solution of this model at this with these values?. Please i need your help. Thank you in advance

secod_code.mw

with*plots; ode1 := (1+1/bet)*(diff(f(eta), eta, eta, eta))-(diff(f(eta), eta))^2+f(eta)*(diff(f(eta), eta, eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1+1/bet)*(diff(diff(diff(f(eta), eta), eta), eta))-(diff(f(eta), eta))^2+f(eta)*(diff(diff(f(eta), eta), eta))+Gr*(theta(eta)+lambda1*theta(eta)^2)+Gc*(phi(eta)+lambda2*phi(eta)^2)-M*(diff(f(eta), eta)) = 0

(1)

ode2 := (diff(theta(eta), eta, eta))*(1+(4*R*(1/3))*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(theta(eta), eta, eta))) = 0

(diff(diff(theta(eta), eta), eta))*(1+(4/3)*R*(theta(eta)+CT)^3)/Pr+4*R*(theta(eta)+CT)^2*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))+Nb*(diff(phi(eta), eta))*(diff(theta(eta), eta))+Nt*(diff(theta(eta), eta))^2-de*(f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(diff(theta(eta), eta), eta))) = 0

(2)

ode3 := diff(phi(eta), eta, eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(theta(eta), eta, eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(phi(eta), eta, eta))) = 0

diff(diff(phi(eta), eta), eta)+Pr*Le*(diff(phi(eta), eta))*f(eta)+Nt*(diff(diff(theta(eta), eta), eta))/Nb-Pr*Le*dc*(f(eta)*(diff(f(eta), eta))*(diff(phi(eta), eta))+f(eta)^2*(diff(diff(phi(eta), eta), eta))) = 0

(3)

(4)

(5)

  for k to 10 do
      sol_All := dsolve
                 ( eval
                   ( {bcs1, ode1, ode2,ode3},
                     [xi= L[k],R=1, CT=0.2, Gr=0.5, Gc=0.5, lambda1=0.2, lambda2=0.2, Pr=0.72, Nb=0.5, Le=1, dc=0.2, de=0.2, Nt=0.5, Zeta=0.5, varsigma=0.5, M=1.5, bet=1.5]
                   ),
                   [f(eta), theta(eta),phi(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]);

phieta || k := rhs(sol_All[8]);
      phipeta || k := rhs(sol_All[7])
  end do:

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

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

Error, invalid subscript selector

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

Error, invalid subscript selector

Error, mismatched or missing bracket/operator

  plot( [ seq((Y_sol||j)(eta), j = 1..6)],
         eta = 0 .. 6,
         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 .. 5,
         labels = [eta, fprime(eta)],
         axes = boxed
      );
plot( [ seq((phipeta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phiprime(eta)],
         axes = boxed
      );

plot( [ seq((phieta||j)(eta), j = 1..6)],
         eta = 0 .. 5,
         labels = [eta, phi(eta)],
         axes = boxed
      );