| Abstract: |
| Burgers equation is a non-linear partial differential equation which occurs in various areas in applied mathematics and can be used to describe physical phenomena such as boundary layer theory. For large Reynolds numbers, the solution of the one-dimensional modified Burgers` equation is characterised by steep gradient and thus can be classified as a singularly perturbed problem. Due to the presence of the steep gradient, classical numerical methods are not able to mimic the behaviour of the exact solutions and thus yield unsatisfactory results.
In this talk, a numerical scheme which is able to resolve the inefficiencies of classical numerical schemes is proposed to solve the modified burgers equation. The stability of the scheme is established and the discretisation error is estimated. Numerical experiments will be conducted to validate any theoretical findings. |
|