(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is a fluid flowing over a hot plate. We non-dimensionalized the problem from three partial diff eq's to two ode's. I am modeling I have two coupled differential equations that are a system of initial value problems. I am supposed to numerically integrate the two equations to come up with values... I'm then told to simplify this to a larger system of first order ode's. I'm not sure how to do this...

2. Relevant equations

I'm given F''' +1/2(F*F'')=0 and G''+Pr/2(F*G')=0 where Pr is the prandle number. F(0)=0 F'(0)=0 F'(infinity)=1 G(0)=1 G(infinity)=0

3. The attempt at a solution

I know I'm supposed to guess F'' and G' to get F' and G' to be what I want them to asymptote to. I just am not sure how to get to a place where I can use something like Runge-Kutta 4th order method...

My attempt was U1=F1 U2=F' U1'=U2=F' U2'=U3=F'' U2''=F''' U2''+1/2(U1*U2')=0

then

V1=U1 V2=U2' V2'=U2'' and V2'+1/2(V1*V2)=0

But I don't know if this is right...

Any help is appreciated thanks,

Matt

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Third order differential equation numerical approximation

**Physics Forums | Science Articles, Homework Help, Discussion**