Numerical solution of one dimensional burgers’ equation solving with explicit FTCS method and implcit BTCS method

Abstract

The turbulent flow in natural phenomena always exist everyday. This dissertation discusses on solving nonlinear of one dimensional Burgers’ equation. The discussion begins with discretizing the equation using two different types of method which are Explicit Forward-Time-Central-Space (FTCS) method and Implicit Backward-Time-Central-Space (BTCS) method. The discretization from both method leads to form an algebraic system. For the case of using explicit FTCS, the system can be solve straightaway since it only consist of one unknown function for the next time step with the known function at previous time step. Apart from that, the discretization of implicit BTCS need to undergo an iterative technique since the system cannot be solve directly. Therefore Newton’s method is used for system of nonlinear equations. Moreover, all numerical computation will be computed in MATLAB programming. The results achieve will be compared with from the journal. In conclusion, the results shows that solving with implicit BTCS are more preferable as it is unconditionally stable which can solve problem without the limitation of time step.