# Question:How to solve the f^(IV) ode problem

## Question:How to solve the f^(IV) ode problem

Greetings,

How solve the f^(IV) ode problem using the Runge Kutterg method

restart; with(plots);
fcns := {f(eta), g(eta), t(eta)};
N := 1; k1 := 5; nb := .3; 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*(diff(t(eta), `\$`(eta, 1)))*(diff(g(eta), `\$`(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 = ["&eta;", "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.

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