# Question:Need help to execute the Maple worksheet

## Question:Need help to execute the Maple worksheet

Maple 11

Hi

I am a PhD scholar at the University of Queensland. I am reviweing a paper titled as "A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition"(the pdf is available online). In this paper the author has written a MAPLE code. I copied the same code in MAPLE but could nt succedded. The author used the Runge Kutta RK5 Method to solve the model.

Please help me to solve the same model in MAPLE by using the RK5 method OR with some other method using Maple. The code is as follows:

>restart: with(plots):

>Eq1:=diff(f(eta),eta,eta,eta)+0.5*f(eta)*diff(f(eta),eta,eta)=0;

>Eq2:=diff(theta(eta),eta,eta)+0.5*Pr*f(eta)*diff(theta(eta),eta)=0;

>bc1:=f(0)=0, D(f)(0)=0, D(f)(10)=1;

>fixedparameter:=Pr=[0.72];

>Eq3:=evalf(Eq2,fixedparameter);

>bc2:=theta(10)=0, D(theta)(0)= -a(1-theta(eta));

>L:=[0.05, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 5, 10, 20];

> for k from 1 to 10 do

>R:=dsolve(eval({Eq1, Eq3, bcs1, bcs2},

a= L[k]), [f(eta), theta(eta)], numeric, output = listprocedure);

Y||k :=rhs(R[5]); Yp||k := -rhs(R[6]);

end do:

>plots([Y||(1..10)],0..6),labels= [eta, theta(eta)]):

>print([Yp||(1. . .10)(0)]);

>print([Y||(1. . .10)(0)]);

﻿