Question: How can I resolve the problem of asking too few boundary conditions ?

Dear All,

I am facing some problems. I want to draw some plots: I have considered the 4th order momentum equation and the 2nd order energy equation; it requires 6 boundary conditions, which I have provided, but till asking for errors (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 6.

eqn1 := {((kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])/(phi[1]+phi[2]+phi[3])+(p-1).kappa[f]+(p-1).(kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])-(p-1).(phi[1]+phi[2]+phi[3]).kappa[f])/((kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])/(phi[1]+phi[2]+phi[3])+(p-1).kappa[f]-(p-1).(kappa[1].phi[1]+kappa[2].phi[2]+kappa[3].phi[3])+(phi[1]+phi[2]+phi[3]).kappa[f]).(diff(theta(eta), eta, eta)+4/3.N.(diff((1+(K-1).theta(eta))^3.(diff(theta(eta), eta)), eta)))+Pr.(((1-phi[3]).((1-phi[2])*(1-phi[1]+phi[1].(`ρc__s1`/`ρc__f`))+phi[2].(`ρc__s2`/`ρc__f`))+phi[3].(`ρc__s3`/`ρc__f`)).(R.f(eta)+alpha.eta).(diff(theta(eta), eta))+Q.theta(eta)+R.Ec.((diff(f(eta), eta, eta))^2)) = 0, diff(f(eta), eta, eta, eta, eta)-(1-phi[1])^2.5.((1-phi[2])^2.5).((1-phi[3])^2.5).((1-phi[3]).((1-phi[2]).(1-phi[1]+phi[1].(`ρ__s1`/`ρ__f`))+phi[2].(`ρ__s2`/`ρ__f`))+phi[3].(`ρ__s3`/`ρ__f`)).(alpha.(eta.(diff(f(eta), eta, eta, eta))+3.*(diff(f(eta), eta, eta)))+(diff(f(eta), eta, eta, eta)).f(eta)-(diff(f(eta), eta)).(diff(f(eta), eta, eta))).R-(1-phi[1])^2.5.((1-phi[2])^2.5).((1-phi[3])^2.5).A.B.e^(-B.eta) = 0, f(-1) = S, f(1) = 1, theta(-1) = 1, theta(1) = 0, (D(f))(-1) = 0, (D(f))(1) = 0}

sys1 := eval(eqn1, {A = 1, B = .5, Ec = .1, K = 1.5, N = .5, Pr = 2, Q = .4, R = 1, S = -.1, p = 3, alpha = .2, `ρ__f` = 997.1, `ρ__s1` = 0, `ρ__s2` = 0, `ρ__s3` = 5180, `ρc__f` = 997.1.4179, `ρc__s1` = 0, `ρc__s2` = 0, `ρc__s3` = 5180.670, phi[1] = 0., phi[2] = 0., phi[3] = 0.3e-1, kappa[1] = 0, kappa[2] = 0, kappa[3] = 9.7, kappa[f] = .613})

sol1 := dsolve(sys1, numeric);
Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 7, got 6
with(plots);
t1 := odeplot(sol1, [eta, diff(f(eta), eta)], eta = -1 .. 1, numpoints = 65, thickness = 0, color = green, linestyle = solid);
plots[plots:-display]({t1})

Download A1.mw