In this paper, we introduce an algorithm to solve the
Advection equation by finite element method. In this method, we
have chosen Three pattern of cubic B-Spline to approximate the
nonlinear solution to convert the nonlinear PDE into a system of
ODE, Then we solved this system equation by SSP-RK54 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 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 work, we present programming solutions for some nonlinear partial differential equations, which are the advection equation, the third-order KdV
equations, and a family of Burgers' equations.
