Need help with newtons method -- CFD Online Discussion Forums

October 24, 2017, 20:12	Need help with newtons method	#1
Fahraynk New Member frank Join Date: Feb 2017 Posts: 8 Rep Power: 9	I have a system which I solved with newtons iteration, and I have to add an additional unknown to the system. The system is the following : $f'''+\frac{m+1}{2} ff''+m(1-(f')^2)=0$ I broke it up into a system of 3 equations: $F_{pp}-F_p''=0$ $F_{pp}'+\frac{m+1}{2}FF_{pp}+m(1-F_p^2)=0$ m is a constant; I set manually set m. Unknowns are f, Fp, Fpp. The equations are approximated with taylor's approximations, and G(x)=0 is the sum of these 3 equations at 1000 grid points + 3 initial conditions. Currently, $X=[f_1...F_{1000},F_{p1}...F_{p1000},F_{pp1}...F_{pp1000}]$ , and I use newtons iteration to solve for X such that G(X)=0 This problem I am trying to solve is this, I am given this information : $H=\frac{\delta}{\theta}$ $\delta=\int_0^\infty(1-F_p) dy$ $\theta=\int_0^\infty(1-F_p)F_p dy$ I am told that I have to take a given H, and use newtons iteration to find m, the constant which I was setting manually before. I want to know, if I change X to $X=[F,F_p,F_{pp},m]$ and then add to G(x), $H-\frac{\delta}{\theta}=H-\frac{\int_0^\infty(1-F_p)}{\int_0^\infty(1-F_p)F_p}$ ,will this be enough for newtons method to solve for m? Or do I have to do something else?

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