Numerical Schemes for Solving One-dimensional Transport Equation

ABSTRACT The numerical manners based on finite element and finite difference methods for solving onedimensional transport equation are presented. The results of both schemes are compared. The finite difference method is developed by replacing the space derivative with the backward difference to obtain a system of differential equation. Finite difference approximation is estimated via Pade′ approximant. The finite difference method is unconditionally stable. Finite element method is applied to obtain system of ordinary differential equation and the system is solved by the forth-order Runge-Kutta method. The numerical approximation of both methods are demonstrated good agreement with the analytical solution