In this paper, we present approximate solutions for the
Advection equation by finite differences method. In this method we
convert the nonlinear partial differential equation into a system of
nonlinear equations by some finite differences methods.
Then this
system was solved by Newton's method. And we made a program
implementing this algorithm and we checked the program using
some examples, which have exact solutions, then we evaluate our
results. As a conclusion we found that this method gives accurate
results for Advection equation.
In this research we study the numerical solution of Burgere
equation by using three methods, The first explicit scheme
method, and the second Crank-Nicolson method, and the thirst
weighted average method for explicit scheme method and Crank-
Nicolson method, Also the studying of numerical stability of all this
methods.
This paper aims to study the distribution of free nitrogen atoms through surface of α – Fe sample using the numerical solution for linear differential equation by means of Crank – Nicolson method at a temperature range ( 550 to 950 0C) and time inter
val (0 – 8)h where the nitrogen diffusion constant is at 850 0C and 8h.
Under the supposed condition this study has illustrated that the diffusion depth of nitrogen atoms from surface towards inners reaches to ̴ 1.2mm, i.e., determining the layer thickness of the formed nitride compounds which gives the surface layer of α – Fe high resistance against corrosion processes resulting from surrounded environment.
