emmantop

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8 years, 193 days

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These are replies submitted by emmantop

@emmantop  rewrite [C] as [C(x)]

@Preben Alsholm Thanks for the suggestion. However, it fails to work.

restart; with(plots);
E := {Ec = .5, Lambda = 3, N = 10, Nr = 2, beta = 0.1e-1, n = 2, sigma = 10, `ε` = .8}; L := [0, .2, .4, .6];
ode1 := (1+Lambda*theta(eta))^2*((diff(f(eta), eta))^2-f(eta)*(diff(f(eta), `$`(eta, 2))))-(1+Lambda*theta(eta))*(diff(f(eta), `$`(eta, 3)))+Lambda*theta(eta)*(diff(f(eta), `$`(eta, 2)))-k[1]*(1+Lambda*theta(eta))^2*(2*(diff(f(eta), eta))*(diff(f(eta), `$`(eta, 3)))+(diff(f(eta), `$`(eta, 2)))^2-f(eta)*(diff(f(eta), `$`(eta, 4)))) = 0;
ode2 := (1+`ε`*theta(eta)+Nr)*(diff(theta(eta), `$`(eta, 2)))+`ε`*(diff(theta(eta), eta))^2+sigma*f(eta)*(diff(theta(eta), eta))+(beta-n*(diff(f(eta), eta)))*sigma*theta(eta)+sigma*Ec((diff(f(eta), eta))^2/(1+Lambda*theta(eta))+k[1]*((diff(f(eta), eta))*(diff(f(eta), `$`(eta, 2)))^2-f(eta)*(diff(f(eta), `$`(eta, 2)))*(diff(f(eta), `$`(eta, 3))))) = 0;
bcs := f(0) = 0, (D(f))(0) = 1, (D(f))(N) = 0, ((D@@2)(f))(N) = 0, theta(0) = 1, theta(N) = 0;

for b in [bcs] do BCS := `minus`({bcs}, {b}); try res[b] := dsolve(eval(`union`({ode1, ode2}, BCS), `union`(E, {k[1]}) = 0), numeric, method = bvp[midrich], abserr = 1.10^(-8)) catch: print*(b, ''failed'') end try end do;
    {theta(0) = 1, theta(N) = 0, D(f)(0) = 1, D(f)(N) = 0,

      @@(D, 2)(f)(N) = 0}
      {f(0) = 0, theta(0) = 1, theta(N) = 0, D(f)(N) = 0,

        @@(D, 2)(f)(N) = 0}
      {f(0) = 0, theta(0) = 1, theta(N) = 0, D(f)(0) = 1,

        @@(D, 2)(f)(N) = 0}
{f(0) = 0, theta(0) = 1, theta(N) = 0, D(f)(0) = 1, D(f)(N) = 0}
      {f(0) = 0, theta(N) = 0, D(f)(0) = 1, D(f)(N) = 0,

        @@(D, 2)(f)(N) = 0}
      {f(0) = 0, theta(0) = 1, D(f)(0) = 1, D(f)(N) = 0,

        @@(D, 2)(f)(N) = 0}
plots:-odeplot(res[(D(f))(0) = 1], [eta, theta(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
plots:-odeplot(res[(D(f))(0) = 1], [eta, f(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
plots:-odeplot(res[(D(f))(N) = 0], [eta, theta(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
plots:-odeplot(res[(D(f))(N) = 0], [eta, f(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

@  Thanks for your suggestion. 

@Carl Love Thanks for your constribution.

@Preben Alsholm Thanks for the insight you gave. I never knew that d[1],..., d[4] values are embedded in the solution when dsolve/bvp[midrich] was used.

Maplesoft needs to give you fellowship.

@Preben Alsholm  The problem corrected still error persist. Sht.mw

@Preben Alsholm  Thank you, I appreciate you.

@Preben Alsholm  Thanks for the assistance. However, how can one carry out the debugging? Or is it peculiar to maple 17?

@Preben Alsholm Thanks, I am thinking of expanding exp(beta/theta) in Taylor series may that we work.

I appreciate you.

@tomleslie  Thank you for your suggestion.

@Preben Alsholm Thank you Preben, I have done what you suggested but the numerical solution returns error. I want to plot analytic and numerical solutions. See the worksheet modify_worksheet.mw

Best regards

 

@Preben Alsholm D is constan while phi[w] is the temperature at the wall.

Thanks.

@Rouben Rostamian  Thanks for the idea, I really appreciate it.

@tomleslie Thanks for the idea.

@Preben Alsholm  I sincerely thank you for taking time to do the error analysis. I will also compare it with the analytic solution for the od1 because I do have the exact solution for it.

Best regards.

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