TO SOLVE NON-LINEAR PDE's OF BVP
in [Matlab]
|
From: sridhar on 2 Jun 2010 21:23 Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1084951456.35015.1272434321031.JavaMail.root(a)gallium.mathforum.org>... > > Given the second order non linear BVP > > > > (ƒ')^n = 1 + γ θ > > …..……………… > > 230;…… 1 > > > > θ" + (λ +n+1/ 2n +1) ƒ θ' - n (2 > > λ +1/2n+ 1) * ƒ' θ = 0 > > ………… 2 > > > > Prime in the above eqn’s describe partial > > differentiation with respect to η > > > > In order to have a PDE, your equation must contain > derivatives with respect to at least two independent > variables. > You say η is one of them. What is the second one, > and where does differentiation with respect to it occur ? > > > Boundary conditions are > > ƒ (0) = 0, θ'(0) = -1 > > ƒ' (∞) = 0, θ(∞) = 0 > > > > can any let me know how the above PDE equations are > > converted to ODE's > > Best wishes > Torsten. Given the second order non linear BVP (ƒ')^n = 1 + γ θ …..……………………… 1 θ" + (λ +n+1/ 2n +1) ƒ θ' - n (2 λ +1/2n+ 1) * ƒ' θ = 0 ………… 2 Prime in the above eqn’s describe partial differentiation with respect to η Boundary conditions are ƒ (0) = 0, θ'(0) = -1 ƒ' (∞) = 0, θ(∞) = 0 where η is a function of x & y given by Similarity variable, η = x ^ (λ-n/2n+1) * y Θ is a dimensionless temperature ƒ is a dimensionless stream function given by Stream function, ψ = x ^ (λ+n+1/2n+1) * ƒ(η) how to solve the above system of PD eqn’s
|
Pages: 1 Prev: Interface with external program: pdftex Next: Augmented Reality in Matlab |