666 jvbasha

javid basha jv

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These are questions asked by 666 jvbasha

Greetings,

How se the f^(IV) ode problem using the Runge metho

 

restart; with(plots);
fcns := {f(eta), gta), t(a)};
N1k1 ;b :; nt 3; pr := 5; sc := 1;
eq1 := diff(f(eta), `$`(eta, 3))+(1/2)*f(eta)*(diff(f(eta), `$`(eta, 2)))+k1*((diff(f(eta), `$`(eta, 1)))*(diff(f(eta), `$`(eta, 3)))-(1/2)*f(eta)*(diff(f(eta), `$`(eta, 4)))+(1/2)*(diff(f(eta), `$`(eta, 2)))^2) = 0; eq2 := diff(t(eta), `$`(eta, 2))+pr*nb*if`ta, 1)))*(diff(g(et`$`(eta, 1)))+pr*nt*(diff(t(eta), `$`(eta, 1^2+(1/2)*f(eta)*(diff(t(eta), `$`(eta, 1))) = 0; eq3 := diff(g(eta), `$`(eta, 2))+nt*(diff(t(eta), `$`(eta, 2)))/nb+(1/2)*f(eta)*(diff(g(eta), `$`(eta, 1)))*sc/pr = 0;
bc := f(0) = 0, (D(f))(0) = 0, (D(f))(N) = 1, ((D@@2)(f))(N) = 0, t(0) = 1, t(N) = 0, g(0) = 1, g(N) = 0;
R := dsolve(eval({bc, eq1, eq2, eq3}), fcns, type = numeric);
Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead
p1u := odeplot(R, [eta, (D(f))(eta)], 0 .. N, numpoints = 100, labels = ["η", "f'"], linestyle = solid, color = [blue], thickness = 1, labeldirections = [horizontal, vertical], labelfont = ['TIMES', 'BOLDOBLIQUE', 16]);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
p1u;


bvp.mw

 

Have a good day.

Dear authors,
How to solve this ode problem.

Download link ode.mw

In this problem the boundary condition is

Note: F=g in our problem.

eta approaches N.

Thank you.

 

in this problem i used slip coundary condition.

the plot want to starts in 0.2, but the plot starts in 0

bc := f(0) = 0, (D(f))(0) = ak*((D^2)(f))(0), (D(f))(N) = 1, g(0) = -de*((D^2)(f))(0), g(N) = 0, T(0) = 1+be*(D(T))(0), T(N) = 0:

How to type double drivative in BC.

ψ =-0.09,-0.07,-0.04,-0.01,0,0.01,0.04,0.07,0.09

these are the ψ values.

then X=

here we can take eta =0..2 and X=-15..15
using this relation how to plot streamlines for eta against X.

Code:
restart; with(plots); fcns := {T(eta), f(eta)}; ep := .1; M := 1; kp := .5; n := 1; ec := .1; pr := 1; s := .1; N := 5; sys := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))*(diff(f(eta), eta))+ep*ep+(M+1/kp)*(ep-(diff(f(eta), eta))) = 0, diff(T(eta), eta, eta)+pr*(f(eta)*(diff(T(eta), eta))-n*(diff(f(eta), eta))*T(eta))+pr*(ec*(diff(f(eta), eta, eta))*(diff(f(eta), eta, eta))+ec*(M+1/kp)*(diff(f(eta), eta))^2+s*T(eta)) = 0; bc := f(0) = 0, (D(f))(0) = 1, (D(f))(N) = ep, T(0) = 1, T(N) = 0; R := dsolve(eval({bc, sys}), numeric, method = bvp[midrich], abserr = 0.1e-9, output = operator); psi = [-0.9e-1, -0.7e-1, -0.4e-1, -0.1e-1, 0, 0.1e-1, 0.4e-1, 0.7e-1, 0.9e-1]; for i to 9 do X[i] = psi[i]/f(eta); print(plots:-contourplot(X[i](X, eta), eta = 0 .. N, X = 0 .. 6)) end do

 


 

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